Complex (Hipparchus 1.7 API)

java.lang.Object
- org.hipparchus.complex.Complex

All Implemented Interfaces:

Serializable, CalculusFieldElement<Complex>, FieldElement<Complex>
```
public class Complex
extends Object
implements CalculusFieldElement<Complex>, Serializable
```
Representation of a Complex number, i.e. a number which has both a real and imaginary part.
Implementations of arithmetic operations handle NaN and infinite values according to the rules for Double, i.e. equals(java.lang.Object) is an equivalence relation for all instances that have a NaN in either real or imaginary part, e.g. the following are considered equal:
- 1 + NaNi
- NaN + i
- NaN + NaNi
Note that this contradicts the IEEE-754 standard for floating point numbers (according to which the test x == x must fail if x is NaN). The method equals for primitive double in Precision conforms with IEEE-754 while this class conforms with the standard behavior for Java object types.
See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`static Complex`	`I` The square root of -1.
`static Complex`	`INF` A complex number representing "+INF + INFi"
`static Complex`	`MINUS_I` The square root of -1.
`static Complex`	`MINUS_ONE` A complex number representing "-1.0 + 0.0i".
`static Complex`	`NaN` A complex number representing "NaN + NaNi".
`static Complex`	`ONE` A complex number representing "1.0 + 0.0i".
`static Complex`	`ZERO` A complex number representing "0.0 + 0.0i".

Fields inherited from interface org.hipparchus.CalculusFieldElement
DEG_TO_RAD, RAD_TO_DEG

Constructor Summary

Constructors
Constructor and Description
`Complex(double real)` Create a complex number given only the real part.
`Complex(double real, double imaginary)` Create a complex number given the real and imaginary parts.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`abs()` Return the absolute value of this complex number.
`Complex`	`acos()` Compute the inverse cosine of this complex number.
`Complex`	`acosh()` Inverse hyperbolic cosine operation.
`Complex`	`add(Complex addend)` Returns a `Complex` whose value is `(this + addend)`.
`Complex`	`add(double addend)` Returns a `Complex` whose value is `(this + addend)`, with `addend` interpreted as a real number.
`Complex`	`asin()` Compute the inverse sine of this complex number.
`Complex`	`asinh()` Inverse hyperbolic sine operation.
`Complex`	`atan()` Compute the inverse tangent of this complex number.
`Complex`	`atan2(Complex x)` Two arguments arc tangent operation.
`Complex`	`atanh()` Inverse hyperbolic tangent operation.
`Complex`	`cbrt()` Cubic root.
`Complex`	`ceil()` Get the smallest whole number larger than instance.
`Complex`	`conjugate()` Returns the conjugate of this complex number.
`Complex`	`copySign(Complex z)` Returns the instance with the sign of the argument.
`Complex`	`copySign(double r)` Returns the instance with the sign of the argument.
`Complex`	`cos()` Compute the cosine of this complex number.
`Complex`	`cosh()` Compute the hyperbolic cosine of this complex number.
`protected Complex`	`createComplex(double realPart, double imaginaryPart)` Create a complex number given the real and imaginary parts.
`Complex`	`divide(Complex divisor)` Returns a `Complex` whose value is `(this / divisor)`.
`Complex`	`divide(double divisor)` Returns a `Complex` whose value is `(this / divisor)`, with `divisor` interpreted as a real number.
`static boolean`	`equals(Complex x, Complex y)` Returns `true` iff the values are equal as defined by `equals(x, y, 1)`.
`static boolean`	`equals(Complex x, Complex y, double eps)` Returns `true` if, both for the real part and for the imaginary part, there is no double value strictly between the arguments or the difference between them is within the range of allowed error (inclusive).
`static boolean`	`equals(Complex x, Complex y, int maxUlps)` Test for the floating-point equality between Complex objects.
`boolean`	`equals(Object other)` Test for equality with another object.
`static boolean`	`equalsWithRelativeTolerance(Complex x, Complex y, double eps)` Returns `true` if, both for the real part and for the imaginary part, there is no double value strictly between the arguments or the relative difference between them is smaller or equal to the given tolerance.
`Complex`	`exp()` Compute the exponential function of this complex number.
`Complex`	`expm1()` Exponential minus 1.
`Complex`	`floor()` Get the largest whole number smaller than instance.
`double`	`getArgument()` Compute the argument of this complex number.
`ComplexField`	`getField()` Get the `Field` to which the instance belongs.
`double`	`getImaginary()` Access the imaginary part.
`double`	`getReal()` Access the real part.
`int`	`hashCode()` Get a hashCode for the complex number.
`Complex`	`hypot(Complex y)` Returns the hypotenuse of a triangle with sides `this` and `y` - sqrt(this² +y²) avoiding intermediate overflow or underflow.
`boolean`	`isInfinite()` Checks whether either the real or imaginary part of this complex number takes an infinite value (either `Double.POSITIVE_INFINITY` or `Double.NEGATIVE_INFINITY`) and neither part is `NaN`.
`boolean`	`isMathematicalInteger()` Check whether the instance is an integer (i.e.
`boolean`	`isNaN()` Checks whether either or both parts of this complex number is `NaN`.
`boolean`	`isReal()` Check whether the instance is real (i.e.
`Complex`	`linearCombination(Complex[] a, Complex[] b)` Compute a linear combination.
`Complex`	`linearCombination(Complex a1, Complex b1, Complex a2, Complex b2)` Compute a linear combination.
`Complex`	`linearCombination(Complex a1, Complex b1, Complex a2, Complex b2, Complex a3, Complex b3)` Compute a linear combination.
`Complex`	`linearCombination(Complex a1, Complex b1, Complex a2, Complex b2, Complex a3, Complex b3, Complex a4, Complex b4)` Compute a linear combination.
`Complex`	`linearCombination(double[] a, Complex[] b)` Compute a linear combination.
`Complex`	`linearCombination(double a1, Complex b1, double a2, Complex b2)` Compute a linear combination.
`Complex`	`linearCombination(double a1, Complex b1, double a2, Complex b2, double a3, Complex b3)` Compute a linear combination.
`Complex`	`linearCombination(double a1, Complex b1, double a2, Complex b2, double a3, Complex b3, double a4, Complex b4)` Compute a linear combination.
`Complex`	`log()` Compute the natural logarithm of this complex number.
`Complex`	`log10()` Base 10 logarithm.
`Complex`	`log1p()` Shifted natural logarithm.
`Complex`	`multiply(Complex factor)` Returns a `Complex` whose value is `this * factor`.
`Complex`	`multiply(double factor)` Returns a `Complex` whose value is `this * factor`, with `factor` interpreted as a real number.
`Complex`	`multiply(int factor)` Returns a `Complex` whose value is `this * factor`, with `factor` interpreted as a integer number.
`Complex`	`negate()` Returns a `Complex` whose value is `(-this)`.
`Complex`	`newInstance(double realPart)` Create an instance corresponding to a constant real value.
`Complex`	`norm()` Return the norm of this complex number.
`List<Complex>`	`nthRoot(int n)` Computes the n-th roots of this complex number.
`Complex`	`pow(Complex x)` Returns of value of this complex number raised to the power of `x`.
`Complex`	`pow(double x)` Returns of value of this complex number raised to the power of `x`.
`Complex`	`pow(int n)` Integer power operation.
`protected Object`	`readResolve()` Resolve the transient fields in a deserialized Complex Object.
`Complex`	`reciprocal()` Returns the multiplicative inverse of `this` element.
`Complex`	`remainder(Complex a)` IEEE remainder operator.
`Complex`	`remainder(double a)` IEEE remainder operator.
`Complex`	`rint()` Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
`Complex`	`rootN(int n)` N^th root.
`Complex`	`scalb(int n)` Multiply the instance by a power of 2.
`Complex`	`signum()` Compute the signum of the instance.
`Complex`	`sin()` Compute the sine of this complex number.
`Complex`	`sinh()` Compute the hyperbolic sine of this complex number.
`Complex`	`sqrt()` Compute the square root of this complex number.
`Complex`	`sqrt1z()` Compute the square root of `1 - this²` for this complex number.
`Complex`	`subtract(Complex subtrahend)` Returns a `Complex` whose value is `(this - subtrahend)`.
`Complex`	`subtract(double subtrahend)` Returns a `Complex` whose value is `(this - subtrahend)`.
`Complex`	`tan()` Compute the tangent of this complex number.
`Complex`	`tanh()` Compute the hyperbolic tangent of this complex number.
`String`	`toString()`
`static Complex`	`valueOf(double realPart)` Create a complex number given only the real part.
`static Complex`	`valueOf(double realPart, double imaginaryPart)` Create a complex number given the real and imaginary parts.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.hipparchus.CalculusFieldElement
getExponent, sinCos, toDegrees, toRadians

- Field Detail
  - I
```
public static final Complex I
```
    The square root of -1. A number representing "0.0 + 1.0i".
  - MINUS_I
```
public static final Complex MINUS_I
```
    The square root of -1. A number representing "0.0 - 1.0i".
    
    Since:
    
    1.7
  - NaN
```
public static final Complex NaN
```
    A complex number representing "NaN + NaNi".
  - INF
```
public static final Complex INF
```
    A complex number representing "+INF + INFi"
  - ONE
```
public static final Complex ONE
```
    A complex number representing "1.0 + 0.0i".
  - MINUS_ONE
```
public static final Complex MINUS_ONE
```
    A complex number representing "-1.0 + 0.0i".
    
    Since:
    
    1.7
  - ZERO
```
public static final Complex ZERO
```
    A complex number representing "0.0 + 0.0i".
- Constructor Detail
  - Complex
```
public Complex(double real)
```
    Create a complex number given only the real part.
    
    Parameters:
    
    real - Real part.
  - Complex
```
public Complex(double real,
               double imaginary)
```
    Create a complex number given the real and imaginary parts.
    
    Parameters:
    
    real - Real part.
    
    imaginary - Imaginary part.
- Method Detail
  - norm
```
public Complex norm()
```
    Return the norm of this complex number. Returns NaN if either real or imaginary part is NaN and Double.POSITIVE_INFINITY if neither part is NaN, but at least one part is infinite.
    
    Returns:
    
    the norm.
    
    Since:
    
    1.7
  - abs
```
public double abs()
```
    Return the absolute value of this complex number. Returns NaN if either real or imaginary part is NaN and Double.POSITIVE_INFINITY if neither part is NaN, but at least one part is infinite.
    
    Returns:
    
    the absolute value.
  - add
```
public Complex add(Complex addend)
            throws NullArgumentException
```
    Returns a Complex whose value is (this + addend). Uses the definitional formula
    (a + bi) + (c + di) = (a+c) + (b+d)i
    If either this or addend has a NaN value in either part, NaN is returned; otherwise Infinite and NaN values are returned in the parts of the result according to the rules for Double arithmetic.
    
    Specified by:
    
    add in interface FieldElement<Complex>
    
    Parameters:
    
    addend - Value to be added to this Complex.
    
    Returns:
    
    this + addend.
    
    Throws:
    
    NullArgumentException - if addend is null.
  - add
```
public Complex add(double addend)
```
    Returns a Complex whose value is (this + addend), with addend interpreted as a real number.
    
    Specified by:
    
    add in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    addend - Value to be added to this Complex.
    
    Returns:
    
    this + addend.
    
    See Also:
    
    add(Complex)
  - conjugate
```
public Complex conjugate()
```
    Returns the conjugate of this complex number. The conjugate of a + bi is a - bi.
    NaN is returned if either the real or imaginary part of this Complex number equals Double.NaN.
    If the imaginary part is infinite, and the real part is not NaN, the returned value has infinite imaginary part of the opposite sign, e.g. the conjugate of 1 + POSITIVE_INFINITY i is 1 - NEGATIVE_INFINITY i.
    
    Returns:
    
    the conjugate of this Complex object.
  - divide
```
public Complex divide(Complex divisor)
               throws NullArgumentException
```
    Returns a Complex whose value is (this / divisor). Implements the definitional formula
```
  
    a + bi          ac + bd + (bc - ad)i
    ----------- = -------------------------
    c + di         c² + d²
  
 
```
    but uses prescaling of operands to limit the effects of overflows and underflows in the computation.
    Infinite and NaN values are handled according to the following rules, applied in the order presented:
    - If either this or divisor has a NaN value in either part, NaN is returned.
    - If divisor equals ZERO, NaN is returned.
    - If this and divisor are both infinite, NaN is returned.
    - If this is finite (i.e., has no Infinite or NaN parts) and divisor is infinite (one or both parts infinite), ZERO is returned.
    - If this is infinite and divisor is finite, NaN values are returned in the parts of the result if the Double rules applied to the definitional formula force NaN results.
    Specified by:
    
    divide in interface FieldElement<Complex>
    
    Parameters:
    
    divisor - Value by which this Complex is to be divided.
    
    Returns:
    
    this / divisor.
    
    Throws:
    
    NullArgumentException - if divisor is null.
  - divide
```
public Complex divide(double divisor)
```
    Returns a Complex whose value is (this / divisor), with divisor interpreted as a real number.
    
    Specified by:
    
    divide in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    divisor - Value by which this Complex is to be divided.
    
    Returns:
    
    this / divisor.
    
    See Also:
    
    divide(Complex)
  - reciprocal
```
public Complex reciprocal()
```
    Returns the multiplicative inverse of this element.
    
    Specified by:
    
    reciprocal in interface CalculusFieldElement<Complex>
    
    Specified by:
    
    reciprocal in interface FieldElement<Complex>
    
    Returns:
    
    the inverse of this.
  - equals
```
public boolean equals(Object other)
```
    Test for equality with another object. If both the real and imaginary parts of two complex numbers are exactly the same, and neither is Double.NaN, the two Complex objects are considered to be equal. The behavior is the same as for JDK's Double:
    - All NaN values are considered to be equal, i.e, if either (or both) real and imaginary parts of the complex number are equal to Double.NaN, the complex number is equal to NaN.
    - Instances constructed with different representations of zero (i.e. either "0" or "-0") are not considered to be equal.
    Overrides:
    
    equals in class Object
    
    Parameters:
    
    other - Object to test for equality with this instance.
    
    Returns:
    
    true if the objects are equal, false if object is null, not an instance of Complex, or not equal to this instance.
  - equals
```
public static boolean equals(Complex x,
                             Complex y,
                             int maxUlps)
```
    Test for the floating-point equality between Complex objects. It returns true if both arguments are equal or within the range of allowed error (inclusive).
    
    Parameters:
    
    x - First value (cannot be null).
    
    y - Second value (cannot be null).
    
    maxUlps - (maxUlps - 1) is the number of floating point values between the real (resp. imaginary) parts of x and y.
    
    Returns:
    
    true if there are fewer than maxUlps floating point values between the real (resp. imaginary) parts of x and y.
    
    See Also:
    
    Precision.equals(double,double,int)
  - equals
```
public static boolean equals(Complex x,
                             Complex y)
```
    Returns true iff the values are equal as defined by equals(x, y, 1).
    
    Parameters:
    
    x - First value (cannot be null).
    
    y - Second value (cannot be null).
    
    Returns:
    
    true if the values are equal.
  - equals
```
public static boolean equals(Complex x,
                             Complex y,
                             double eps)
```
    Returns true if, both for the real part and for the imaginary part, there is no double value strictly between the arguments or the difference between them is within the range of allowed error (inclusive). Returns false if either of the arguments is NaN.
    
    Parameters:
    
    x - First value (cannot be null).
    
    y - Second value (cannot be null).
    
    eps - Amount of allowed absolute error.
    
    Returns:
    
    true if the values are two adjacent floating point numbers or they are within range of each other.
    
    See Also:
    
    Precision.equals(double,double,double)
  - equalsWithRelativeTolerance
```
public static boolean equalsWithRelativeTolerance(Complex x,
                                                  Complex y,
                                                  double eps)
```
    Returns true if, both for the real part and for the imaginary part, there is no double value strictly between the arguments or the relative difference between them is smaller or equal to the given tolerance. Returns false if either of the arguments is NaN.
    
    Parameters:
    
    x - First value (cannot be null).
    
    y - Second value (cannot be null).
    
    eps - Amount of allowed relative error.
    
    Returns:
    
    true if the values are two adjacent floating point numbers or they are within range of each other.
    
    See Also:
    
    Precision.equalsWithRelativeTolerance(double,double,double)
  - hashCode
```
public int hashCode()
```
    Get a hashCode for the complex number. Any Double.NaN value in real or imaginary part produces the same hash code 7.
    
    Overrides:
    
    hashCode in class Object
    
    Returns:
    
    a hash code value for this object.
  - getImaginary
```
public double getImaginary()
```
    Access the imaginary part.
    
    Returns:
    
    the imaginary part.
  - getReal
```
public double getReal()
```
    Access the real part.
    
    Specified by:
    
    getReal in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the real part.
  - isNaN
```
public boolean isNaN()
```
    Checks whether either or both parts of this complex number is NaN.
    
    Specified by:
    
    isNaN in interface CalculusFieldElement<Complex>
    
    Returns:
    
    true if either or both parts of this complex number is NaN; false otherwise.
  - isReal
```
public boolean isReal()
```
    Check whether the instance is real (i.e. imaginary part is zero).
    
    Returns:
    
    true if imaginary part is zero
    
    Since:
    
    1.7
  - isMathematicalInteger
```
public boolean isMathematicalInteger()
```
    Check whether the instance is an integer (i.e. imaginary part is zero and real part has no fractional part).
    
    Returns:
    
    true if imaginary part is zero and real part has no fractional part
    
    Since:
    
    1.7
  - isInfinite
```
public boolean isInfinite()
```
    Checks whether either the real or imaginary part of this complex number takes an infinite value (either Double.POSITIVE_INFINITY or Double.NEGATIVE_INFINITY) and neither part is NaN.
    
    Specified by:
    
    isInfinite in interface CalculusFieldElement<Complex>
    
    Returns:
    
    true if one or both parts of this complex number are infinite and neither part is NaN.
  - multiply
```
public Complex multiply(Complex factor)
                 throws NullArgumentException
```
    Returns a Complex whose value is this * factor. Implements preliminary checks for NaN and infinity followed by the definitional formula:
    (a + bi)(c + di) = (ac - bd) + (ad + bc)i
    Returns NaN if either this or factor has one or more NaN parts.
    Returns INF if neither this nor factor has one or more NaN parts and if either this or factor has one or more infinite parts (same result is returned regardless of the sign of the components).
    Returns finite values in components of the result per the definitional formula in all remaining cases.
    
    Specified by:
    
    multiply in interface FieldElement<Complex>
    
    Parameters:
    
    factor - value to be multiplied by this Complex.
    
    Returns:
    
    this * factor.
    
    Throws:
    
    NullArgumentException - if factor is null.
  - multiply
```
public Complex multiply(int factor)
```
    Returns a Complex whose value is this * factor, with factor interpreted as a integer number.
    
    Specified by:
    
    multiply in interface FieldElement<Complex>
    
    Parameters:
    
    factor - value to be multiplied by this Complex.
    
    Returns:
    
    this * factor.
    
    See Also:
    
    multiply(Complex)
  - multiply
```
public Complex multiply(double factor)
```
    Returns a Complex whose value is this * factor, with factor interpreted as a real number.
    
    Specified by:
    
    multiply in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    factor - value to be multiplied by this Complex.
    
    Returns:
    
    this * factor.
    
    See Also:
    
    multiply(Complex)
  - negate
```
public Complex negate()
```
    Returns a Complex whose value is (-this). Returns NaN if either real or imaginary part of this Complex number is Double.NaN.
    
    Specified by:
    
    negate in interface FieldElement<Complex>
    
    Returns:
    
    -this.
  - subtract
```
public Complex subtract(Complex subtrahend)
                 throws NullArgumentException
```
    Returns a Complex whose value is (this - subtrahend). Uses the definitional formula
    (a + bi) - (c + di) = (a-c) + (b-d)i
    If either this or subtrahend has a NaN] value in either part, NaN is returned; otherwise infinite and NaN values are returned in the parts of the result according to the rules for Double arithmetic.
    
    Specified by:
    
    subtract in interface FieldElement<Complex>
    
    Parameters:
    
    subtrahend - value to be subtracted from this Complex.
    
    Returns:
    
    this - subtrahend.
    
    Throws:
    
    NullArgumentException - if subtrahend is null.
  - subtract
```
public Complex subtract(double subtrahend)
```
    Returns a Complex whose value is (this - subtrahend).
    
    Specified by:
    
    subtract in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    subtrahend - value to be subtracted from this Complex.
    
    Returns:
    
    this - subtrahend.
    
    See Also:
    
    subtract(Complex)
  - acos
```
public Complex acos()
```
    Compute the inverse cosine of this complex number. Implements the formula:
    acos(z) = -i (log(z + i (sqrt(1 - z<sup>2</sup>))))
    Returns NaN if either real or imaginary part of the input argument is NaN or infinite.
    
    Specified by:
    
    acos in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the inverse cosine of this complex number.
  - asin
```
public Complex asin()
```
    Compute the inverse sine of this complex number. Implements the formula:
    asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz))
    Returns NaN if either real or imaginary part of the input argument is NaN or infinite.
    
    Specified by:
    
    asin in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the inverse sine of this complex number.
  - atan
```
public Complex atan()
```
    Compute the inverse tangent of this complex number. Implements the formula:
    atan(z) = (i/2) log((i + z)/(i - z))
    Returns NaN if either real or imaginary part of the input argument is NaN or infinite.
    
    Specified by:
    
    atan in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the inverse tangent of this complex number
  - cos
```
public Complex cos()
```
    Compute the cosine of this complex number. Implements the formula:
    cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i
    where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
```
  Examples:
  
   cos(1 ± INFINITY i) = 1 ∓ INFINITY i
   cos(±INFINITY + i) = NaN + NaN i
   cos(±INFINITY ± INFINITY i) = NaN + NaN i
  
 
```
    Specified by:
    
    cos in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the cosine of this complex number.
  - cosh
```
public Complex cosh()
```
    Compute the hyperbolic cosine of this complex number. Implements the formula:
```
  
   cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i
  
 
```
    where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
```
  Examples:
  
   cosh(1 ± INFINITY i) = NaN + NaN i
   cosh(±INFINITY + i) = INFINITY ± INFINITY i
   cosh(±INFINITY ± INFINITY i) = NaN + NaN i
  
 
```
    Specified by:
    
    cosh in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the hyperbolic cosine of this complex number.
  - exp
```
public Complex exp()
```
    Compute the exponential function of this complex number. Implements the formula:
```
  
   exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i
  
 
```
    where the (real) functions on the right-hand side are FastMath.exp(double), FastMath.cos(double), and FastMath.sin(double).
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
```
  Examples:
  
   exp(1 ± INFINITY i) = NaN + NaN i
   exp(INFINITY + i) = INFINITY + INFINITY i
   exp(-INFINITY + i) = 0 + 0i
   exp(±INFINITY ± INFINITY i) = NaN + NaN i
  
 
```
    Specified by:
    
    exp in interface CalculusFieldElement<Complex>
    
    Returns:
    
    e^this.
  - expm1
```
public Complex expm1()
```
    Exponential minus 1.
    
    Specified by:
    
    expm1 in interface CalculusFieldElement<Complex>
    
    Returns:
    
    exponential minus one of the instance
    
    Since:
    
    1.7
  - log
```
public Complex log()
```
    Compute the natural logarithm of this complex number. Implements the formula:
```
  
   log(a + bi) = ln(|a + bi|) + arg(a + bi)i
  
 
```
    where ln on the right hand side is FastMath.log(double), |a + bi| is the modulus, abs(), and arg(a + bi) = FastMath.atan2(double, double)(b, a).
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite (or critical) values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
```
  Examples:
  
   log(1 ± INFINITY i) = INFINITY ± (π/2)i
   log(INFINITY + i) = INFINITY + 0i
   log(-INFINITY + i) = INFINITY + πi
   log(INFINITY ± INFINITY i) = INFINITY ± (π/4)i
   log(-INFINITY ± INFINITY i) = INFINITY ± (3π/4)i
   log(0 + 0i) = -INFINITY + 0i
  
 
```
    Specified by:
    
    log in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the value ln this, the natural logarithm of this.
  - log1p
```
public Complex log1p()
```
    Shifted natural logarithm.
    
    Specified by:
    
    log1p in interface CalculusFieldElement<Complex>
    
    Returns:
    
    logarithm of one plus the instance
    
    Since:
    
    1.7
  - log10
```
public Complex log10()
```
    Base 10 logarithm.
    
    Specified by:
    
    log10 in interface CalculusFieldElement<Complex>
    
    Returns:
    
    base 10 logarithm of the instance
    
    Since:
    
    1.7
  - pow
```
public Complex pow(Complex x)
            throws NullArgumentException
```
    Returns of value of this complex number raised to the power of x.
    If x is a real number whose real part has an integer value, returns pow(int), if both this and x are real and FastMath.pow(double, double) with the corresponding real arguments would return a finite number (neither NaN nor infinite), then returns the same value converted to Complex, with the same special cases. In all other cases real cases, implements y^x = exp(x·log(y)).
    
    Specified by:
    
    pow in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    x - exponent to which this Complex is to be raised.
    
    Returns:
    
    this^x.
    
    Throws:
    
    NullArgumentException - if x is null.
  - pow
```
public Complex pow(double x)
```
    Returns of value of this complex number raised to the power of x.
    If x has an integer value, returns pow(int), if this is real and FastMath.pow(double, double) with the corresponding real arguments would return a finite number (neither NaN nor infinite), then returns the same value converted to Complex, with the same special cases. In all other cases real cases, implements y^x = exp(x·log(y)).
    
    Specified by:
    
    pow in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    x - exponent to which this Complex is to be raised.
    
    Returns:
    
    this^x.
  - pow
```
public Complex pow(int n)
```
    Integer power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
    
    Since:
    
    1.7
  - sin
```
public Complex sin()
```
    Compute the sine of this complex number. Implements the formula:
```
  
   sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i
  
 
```
    where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
```
  Examples:
  
   sin(1 ± INFINITY i) = 1 ± INFINITY i
   sin(±INFINITY + i) = NaN + NaN i
   sin(±INFINITY ± INFINITY i) = NaN + NaN i
  
 
```
    Specified by:
    
    sin in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the sine of this complex number.
  - atan2
```
public Complex atan2(Complex x)
```
    Two arguments arc tangent operation.
    
    Specified by:
    
    atan2 in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(this, x)
    
    Since:
    
    1.7
  - acosh
```
public Complex acosh()
```
    Inverse hyperbolic cosine operation.
    Branch cuts are on the real axis, below +1.
    
    Specified by:
    
    acosh in interface CalculusFieldElement<Complex>
    
    Returns:
    
    acosh(this)
    
    Since:
    
    1.7
  - asinh
```
public Complex asinh()
```
    Inverse hyperbolic sine operation.
    Branch cuts are on the imaginary axis, above +i and below -i.
    
    Specified by:
    
    asinh in interface CalculusFieldElement<Complex>
    
    Returns:
    
    asin(this)
    
    Since:
    
    1.7
  - atanh
```
public Complex atanh()
```
    Inverse hyperbolic tangent operation.
    Branch cuts are on the real axis, above +1 and below -1.
    
    Specified by:
    
    atanh in interface CalculusFieldElement<Complex>
    
    Returns:
    
    atanh(this)
    
    Since:
    
    1.7
  - sinh
```
public Complex sinh()
```
    Compute the hyperbolic sine of this complex number. Implements the formula:
```
  
   sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i
  
 
```
    where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
```
  Examples:
  
   sinh(1 ± INFINITY i) = NaN + NaN i
   sinh(±INFINITY + i) = ± INFINITY + INFINITY i
   sinh(±INFINITY ± INFINITY i) = NaN + NaN i
  
 
```
    Specified by:
    
    sinh in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the hyperbolic sine of this.
  - sqrt
```
public Complex sqrt()
```
    Compute the square root of this complex number. Implements the following algorithm to compute sqrt(a + bi):
    1. Let t = sqrt((|a| + |a + bi|) / 2)
    2. if a ≥ 0 return t + (b/2t)i else return |b|/2t + sign(b)t i
    where
    - |a| = FastMath.abs(int)(a)
    - |a + bi| = abs()(a + bi)
    - sign(b) = copySign(1d, b)
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
```
  Examples:
  
   sqrt(1 ± INFINITY i) = INFINITY + NaN i
   sqrt(INFINITY + i) = INFINITY + 0i
   sqrt(-INFINITY + i) = 0 + INFINITY i
   sqrt(INFINITY ± INFINITY i) = INFINITY + NaN i
   sqrt(-INFINITY ± INFINITY i) = NaN ± INFINITY i
  
 
```
    Specified by:
    
    sqrt in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the square root of this.
  - sqrt1z
```
public Complex sqrt1z()
```
    Compute the square root of 1 - this² for this complex number. Computes the result directly as sqrt(ONE.subtract(z.multiply(z))).
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
    
    Returns:
    
    the square root of 1 - this².
  - cbrt
```
public Complex cbrt()
```
    Cubic root.
    This implementation compute the principal cube root by using a branch cut along real negative axis.
    
    Specified by:
    
    cbrt in interface CalculusFieldElement<Complex>
    
    Returns:
    
    cubic root of the instance
    
    Since:
    
    1.7
  - rootN
```
public Complex rootN(int n)
```
    N^th root.
    This implementation compute the principal n^th root by using a branch cut along real negative axis.
    
    Specified by:
    
    rootN in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    n - order of the root
    
    Returns:
    
    n^th root of the instance
    
    Since:
    
    1.7
  - tan
```
public Complex tan()
```
    Compute the tangent of this complex number. Implements the formula:
```
  
   tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i
  
 
```
    where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite (or critical) values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
```
  Examples:
  
   tan(a ± INFINITY i) = 0 ± i
   tan(±INFINITY + bi) = NaN + NaN i
   tan(±INFINITY ± INFINITY i) = NaN + NaN i
   tan(±π/2 + 0 i) = ±INFINITY + NaN i
  
 
```
    Specified by:
    
    tan in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the tangent of this.
  - tanh
```
public Complex tanh()
```
    Compute the hyperbolic tangent of this complex number. Implements the formula:
```
  
   tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i
  
 
```
    where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).
    Returns NaN if either real or imaginary part of the input argument is NaN.
    Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.
```
  Examples:
  
   tanh(a ± INFINITY i) = NaN + NaN i
   tanh(±INFINITY + bi) = ±1 + 0 i
   tanh(±INFINITY ± INFINITY i) = NaN + NaN i
   tanh(0 + (π/2)i) = NaN + INFINITY i
  
 
```
    Specified by:
    
    tanh in interface CalculusFieldElement<Complex>
    
    Returns:
    
    the hyperbolic tangent of this.
  - getArgument
```
public double getArgument()
```
    Compute the argument of this complex number. The argument is the angle phi between the positive real axis and the point representing this number in the complex plane. The value returned is between -PI (not inclusive) and PI (inclusive), with negative values returned for numbers with negative imaginary parts.
    If either real or imaginary part (or both) is NaN, NaN is returned. Infinite parts are handled as Math.atan2 handles them, essentially treating finite parts as zero in the presence of an infinite coordinate and returning a multiple of pi/4 depending on the signs of the infinite parts. See the javadoc for Math.atan2 for full details.
    
    Returns:
    
    the argument of this.
  - nthRoot
```
public List<Complex> nthRoot(int n)
                      throws MathIllegalArgumentException
```
    Computes the n-th roots of this complex number. The nth roots are defined by the formula:
```
  
   z_k = abs^1/n (cos(phi + 2πk/n) + i (sin(phi + 2πk/n))
  
 
```
    for k=0, 1, ..., n-1, where abs and phi are respectively the modulus and argument of this complex number.
    If one or both parts of this complex number is NaN, a list with just one element, NaN is returned. if neither part is NaN, but at least one part is infinite, the result is a one-element list containing INF.
    Parameters:
    
    n - Degree of root.
    
    Returns:
    
    a List of all n-th roots of this.
    
    Throws:
    
    MathIllegalArgumentException - if n <= 0.
  - createComplex
```
protected Complex createComplex(double realPart,
                                double imaginaryPart)
```
    Create a complex number given the real and imaginary parts.
    
    Parameters:
    
    realPart - Real part.
    
    imaginaryPart - Imaginary part.
    
    Returns:
    
    a new complex number instance.
    
    See Also:
    
    valueOf(double, double)
  - valueOf
```
public static Complex valueOf(double realPart,
                              double imaginaryPart)
```
    Create a complex number given the real and imaginary parts.
    
    Parameters:
    
    realPart - Real part.
    
    imaginaryPart - Imaginary part.
    
    Returns:
    
    a Complex instance.
  - valueOf
```
public static Complex valueOf(double realPart)
```
    Create a complex number given only the real part.
    
    Parameters:
    
    realPart - Real part.
    
    Returns:
    
    a Complex instance.
  - newInstance
```
public Complex newInstance(double realPart)
```
    Create an instance corresponding to a constant real value.
    The default implementation creates the instance by adding the value to getField().getZero(). This is not optimal and does not work when called with a negative zero as the sign of zero is lost with the addition. The default implementation should therefore be overridden in concrete classes. The default implementation will be removed at the next major version.
    
    Specified by:
    
    newInstance in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    realPart - constant real value
    
    Returns:
    
    instance corresponding to a constant real value
  - readResolve
```
protected final Object readResolve()
```
    Resolve the transient fields in a deserialized Complex Object. Subclasses will need to override createComplex(double, double) to deserialize properly.
    
    Returns:
    
    A Complex instance with all fields resolved.
  - getField
```
public ComplexField getField()
```
    Get the Field to which the instance belongs.
    
    Specified by:
    
    getField in interface FieldElement<Complex>
    
    Returns:
    
    Field to which the instance belongs
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - scalb
```
public Complex scalb(int n)
```
    Multiply the instance by a power of 2.
    
    Specified by:
    
    scalb in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
    
    Since:
    
    1.7
  - hypot
```
public Complex hypot(Complex y)
```
    Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.
    - If either argument is infinite, then the result is positive infinity.
    - else, if either argument is NaN then the result is NaN.
    Specified by:
    
    hypot in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    y - a value
    
    Returns:
    
    sqrt(this² +y²)
    
    Since:
    
    1.7
  - linearCombination
```
public Complex linearCombination(Complex[] a,
                                 Complex[] b)
                          throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if arrays dimensions don't match
    
    Since:
    
    1.7
  - linearCombination
```
public Complex linearCombination(double[] a,
                                 Complex[] b)
                          throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if arrays dimensions don't match
    
    Since:
    
    1.7
  - linearCombination
```
public Complex linearCombination(Complex a1,
                                 Complex b1,
                                 Complex a2,
                                 Complex b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    Returns:
    
    a₁×b₁ + a₂×b₂
    
    Since:
    
    1.7
    
    See Also:
    
    CalculusFieldElement.linearCombination(Object, Object, Object, Object, Object, Object), CalculusFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
  - linearCombination
```
public Complex linearCombination(double a1,
                                 Complex b1,
                                 double a2,
                                 Complex b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    Returns:
    
    a₁×b₁ + a₂×b₂
    
    Since:
    
    1.7
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, Object, double, Object, double, Object), CalculusFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)
  - linearCombination
```
public Complex linearCombination(Complex a1,
                                 Complex b1,
                                 Complex a2,
                                 Complex b2,
                                 Complex a3,
                                 Complex b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    Since:
    
    1.7
    
    See Also:
    
    CalculusFieldElement.linearCombination(Object, Object, Object, Object), CalculusFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
  - linearCombination
```
public Complex linearCombination(double a1,
                                 Complex b1,
                                 double a2,
                                 Complex b2,
                                 double a3,
                                 Complex b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    Since:
    
    1.7
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, Object, double, Object), CalculusFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)
  - linearCombination
```
public Complex linearCombination(Complex a1,
                                 Complex b1,
                                 Complex a2,
                                 Complex b2,
                                 Complex a3,
                                 Complex b3,
                                 Complex a4,
                                 Complex b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    a4 - first factor of the fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    Since:
    
    1.7
    
    See Also:
    
    CalculusFieldElement.linearCombination(Object, Object, Object, Object), CalculusFieldElement.linearCombination(Object, Object, Object, Object, Object, Object)
  - linearCombination
```
public Complex linearCombination(double a1,
                                 Complex b1,
                                 double a2,
                                 Complex b2,
                                 double a3,
                                 Complex b3,
                                 double a4,
                                 Complex b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    a4 - first factor of the fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    Since:
    
    1.7
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, Object, double, Object), CalculusFieldElement.linearCombination(double, Object, double, Object, double, Object)
  - ceil
```
public Complex ceil()
```
    Get the smallest whole number larger than instance.
    
    Specified by:
    
    ceil in interface CalculusFieldElement<Complex>
    
    Returns:
    
    ceil(this)
    
    Since:
    
    1.7
  - floor
```
public Complex floor()
```
    Get the largest whole number smaller than instance.
    
    Specified by:
    
    floor in interface CalculusFieldElement<Complex>
    
    Returns:
    
    floor(this)
    
    Since:
    
    1.7
  - rint
```
public Complex rint()
```
    Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
    
    Specified by:
    
    rint in interface CalculusFieldElement<Complex>
    
    Returns:
    
    a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
    
    Since:
    
    1.7
  - remainder
```
public Complex remainder(double a)
```
    IEEE remainder operator.
    for complex numbers, the integer n corresponding to this.subtract(remainder(a)).divide(a) is a Wikipedia - Gaussian integer.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
    
    Since:
    
    1.7
  - remainder
```
public Complex remainder(Complex a)
```
    IEEE remainder operator.
    for complex numbers, the integer n corresponding to this.subtract(remainder(a)).divide(a) is a Wikipedia - Gaussian integer.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
    
    Since:
    
    1.7
  - signum
```
public Complex signum()
```
    Compute the signum of the instance. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
    
    Specified by:
    
    signum in interface CalculusFieldElement<Complex>
    
    Returns:
    
    -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
    
    Since:
    
    1.7
  - copySign
```
public Complex copySign(Complex z)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    The signs of real and imaginary parts are copied independently.
    
    Specified by:
    
    copySign in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    z - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
    
    Since:
    
    1.7
  - copySign
```
public Complex copySign(double r)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface CalculusFieldElement<Complex>
    
    Parameters:
    
    r - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
    
    Since:
    
    1.7

Class Complex

Field Summary

Fields inherited from interface org.hipparchus.CalculusFieldElement

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

Field Detail

I

MINUS_I

NaN

INF

ONE

MINUS_ONE

ZERO

Constructor Detail

Complex

Complex

Method Detail

norm

abs

add

add

conjugate

divide

divide

reciprocal

equals

equals

equals

equals

equalsWithRelativeTolerance

hashCode

getImaginary

getReal

isNaN

isReal

isMathematicalInteger

isInfinite

multiply

multiply

multiply

negate

subtract

subtract

acos

asin

atan

cos

cosh

exp

expm1

log

log1p

log10

pow

pow

pow

sin

atan2

acosh

asinh

atanh

sinh

sqrt

sqrt1z

cbrt

rootN

tan

tanh

getArgument

nthRoot

createComplex

valueOf

valueOf

newInstance

readResolve

getField

toString

scalb