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

```
public class Complex
extends Object
```
Complex.java. Immutable complex numbers. This implementation stores the real and imaginary component as a double value. These fields are directly accessible, or through a getter. There are also getters for the norm and phi, but this are a CPU intensive.
Copyright (c) 2021-2021 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
BSD-style license. See DJUTILS License.

Author:

Alexander Verbraeck, Peter Knoppers

Field Summary

Fields
Modifier and Type	Field	Description
`static Complex`	`I`	The imaginary unit value (i).
`double`	`im`	Imaginary component.
`static Complex`	`MINUS_I`	The negative imaginary unit value (i).
`static Complex`	`MINUS_ONE`	The (real) minus one value in the complex number space.
`static Complex`	`ONE`	The (real) one value in the complex number space.
`double`	`re`	Real component.
`static Complex`	`ZERO`	The zero value in the complex number space.

Constructor Summary

Constructors
Constructor	Description
`Complex(double re)`	Construct a new complex number with specified real component and zero imaginary component.
`Complex(double re, double im)`	Construct a new complex number.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`Complex`	`conjugate()`	Construct the complex conjugate of this Complex.
`Complex`	`divideBy(double rightOperand)`	Divide this Complex by a scalar.
`Complex`	`divideBy(Complex rightOperand)`	Divide this Complex by another Complex.
`boolean`	`equals(Object obj)`
`double`	`getIm()`	Retrieve the imaginary component of this complex number.
`double`	`getRe()`	Retrieve the real component of this complex number.
`int`	`hashCode()`
`static double`	`hypot(double x, double y)`	Better implementation of the hypotenuse function (faster and more accurate than the one in the java Math library).
`boolean`	`isImaginary()`	Determine if this Complex has a real component of zero.
`boolean`	`isReal()`	Determine if this Complex has an imaginary component of zero.
`Complex`	`minus(double rightOperand)`	Subtract a scalar from this Complex.
`Complex`	`minus(Complex rightOperand)`	Subtract another Complex from this Complex.
`double`	`norm()`	Compute and return the norm, or radius, or absolute value of this complex number.
`double`	`phi()`	Compute and return the phase or phi of this complex number.
`Complex`	`plus(double rightOperand)`	Add a scalar to this Complex.
`Complex`	`plus(Complex rightOperand)`	Add this Complex and another Complex.
`Complex`	`reciprocal()`	Compute the reciprocal of this Complex.
`Complex`	`rotate(double angle)`	Rotate this Complex by an angle.
`Complex`	`times(double rightOperand)`	Multiply this Complex with a scalar.
`Complex`	`times(Complex rightOperand)`	Multiply this Complex with another Complex.
`String`	`toString()`

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

- Field Detail
  - re
```
public final double re
```
    Real component.
  - im
```
public final double im
```
    Imaginary component.
  - ZERO
```
public static final Complex ZERO
```
    The zero value in the complex number space.
  - ONE
```
public static final Complex ONE
```
    The (real) one value in the complex number space.
  - MINUS_ONE
```
public static final Complex MINUS_ONE
```
    The (real) minus one value in the complex number space.
  - I
```
public static final Complex I
```
    The imaginary unit value (i).
  - MINUS_I
```
public static final Complex MINUS_I
```
    The negative imaginary unit value (i).
- Constructor Detail
  - Complex
```
public Complex(double re,
               double im)
```
    Construct a new complex number.
    
    Parameters:
    
    re - double; real component of the new complex number
    
    im - double; imaginary component of the new complex number
  - Complex
```
public Complex(double re)
```
    Construct a new complex number with specified real component and zero imaginary component.
    
    Parameters:
    
    re - double; the real component of the new complex number
- Method Detail
  - getRe
```
public double getRe()
```
    Retrieve the real component of this complex number.
    
    Returns:
    
    double; the real component of this complex number
  - getIm
```
public double getIm()
```
    Retrieve the imaginary component of this complex number.
    
    Returns:
    
    double; the imaginary component of this complex number
  - norm
```
public double norm()
```
    Compute and return the norm, or radius, or absolute value of this complex number.
    
    Returns:
    
    double; the norm, or radius, or absolute value of this complex number. Due to the fact that in this implementation of complex numbers, all values are stored as a real an imaginary double value; the result may overflow to Double.POSITIVE_INFINITY, even though both the real and imaginary part of the complex number can be represented.
  - hypot
```
public static double hypot(double x,
                           double y)
```
    Better implementation of the hypotenuse function (faster and more accurate than the one in the java Math library).
    Derived from An improved algorithm for hypot(a, b) by Carlos F. Borges.
    
    Parameters:
    
    x - double; the x value
    
    y - double; the y value
    
    Returns:
    
    double; hypot(x, y)
  - phi
```
public double phi()
```
    Compute and return the phase or phi of this complex number.
    
    Returns:
    
    double; the phase or phi of this complex number in Radians. Due to the fact that in this implementation of complex numbers, all values are stored as a real and imaginary value; the result of this method is always normalized to the interval (-π,π].
  - isReal
```
public boolean isReal()
```
    Determine if this Complex has an imaginary component of zero.
    
    Returns:
    
    boolean; true if the imaginary component of this Complex number is 0.0; false if the imaginary component of this Complex number is not 0.0.
  - isImaginary
```
public boolean isImaginary()
```
    Determine if this Complex has a real component of zero.
    
    Returns:
    
    boolean; true if the real component of this Complex number is 0.0; false if the real component of this Complex number is not 0.0
  - conjugate
```
public Complex conjugate()
```
    Construct the complex conjugate of this Complex.
    
    Returns:
    
    Complex; the complex conjugate of this
  - rotate
```
public Complex rotate(double angle)
```
    Rotate this Complex by an angle.
    
    Parameters:
    
    angle - double; the angle (in Radians)
    
    Returns:
    
    complex; the result of the rotation
  - plus
```
public Complex plus(Complex rightOperand)
```
    Add this Complex and another Complex.
    
    Parameters:
    
    rightOperand - Complex; the other Complex
    
    Returns:
    
    Complex; the sum of this Complex and the other Complex
  - plus
```
public Complex plus(double rightOperand)
```
    Add a scalar to this Complex.
    
    Parameters:
    
    rightOperand - double; the scalar
    
    Returns:
    
    Complex; the sum of this Complex and the scalar
  - minus
```
public Complex minus(Complex rightOperand)
```
    Subtract another Complex from this Complex.
    
    Parameters:
    
    rightOperand - Complex; the other Complex
    
    Returns:
    
    Complex; the difference of this Complex and the other Complex
  - minus
```
public Complex minus(double rightOperand)
```
    Subtract a scalar from this Complex.
    
    Parameters:
    
    rightOperand - double; the scalar
    
    Returns:
    
    Complex; the difference of this Complex and the scalar
  - times
```
public Complex times(Complex rightOperand)
```
    Multiply this Complex with another Complex.
    
    Parameters:
    
    rightOperand - Complex; the right hand side operand
    
    Returns:
    
    Complex; the product of this Complex and the other Complex
  - times
```
public Complex times(double rightOperand)
```
    Multiply this Complex with a scalar.
    
    Parameters:
    
    rightOperand - double; the right hand side operand
    
    Returns:
    
    Complex; the product of this Complex and the scalar
  - reciprocal
```
public Complex reciprocal()
```
    Compute the reciprocal of this Complex. If this is zero, the result will have the re field set to Double.POSITIVE_INFINITY and the imaginary part set to NEGATIVE_INFINITY.
    
    Returns:
    
    Complex; the reciprocal of this Complex (1 / this)
  - divideBy
```
public Complex divideBy(Complex rightOperand)
```
    Divide this Complex by another Complex. Division by ZERO yields a Complex with re set to Infinity if this.re != 0 and NaN if this.re == 0 and im set to Infinity if this.im != 0 and NaN if this.im == 0.
    
    Parameters:
    
    rightOperand - Complex; the right hand side operand
    
    Returns:
    
    Complex; the ratio of this Complex and the right hand side operand
  - divideBy
```
public Complex divideBy(double rightOperand)
```
    Divide this Complex by a scalar. Division by 0.0 yields a Complex with re set to Infinity if this.re != 0 and NaN if this.re == 0 and im set to Infinity if this.im != 0 and NaN if this.im == 0.
    
    Parameters:
    
    rightOperand - double; the scalar right hand side operand
    
    Returns:
    
    Complex; the ratio of this Complex and the right hand side operand
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class Object
  - equals
```
public boolean equals(Object obj)
```
    Overrides:
    
    equals in class Object

Class Complex

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

re

im

ZERO

ONE

MINUS_ONE

I

MINUS_I

Constructor Detail

Complex

Complex

Method Detail

getRe

getIm

norm

hypot

phi

isReal

isImaginary

conjugate

rotate

plus

plus

minus

minus

times

times

reciprocal

divideBy

divideBy

toString

hashCode

equals