Complex

java.lang.Object
- ptolemy.math.Complex

```
public class Complex
extends java.lang.Object
```
This class provides a complex data type and a library of functions that operate on and return complex numbers. An instance of the class is immutable, meaning that its value is set in the constructor and cannot then be modified. This is similar to the Java built-in classes like Double, Integer, etc.
Although this code is written from scratch, I looked at several designs and borrowed elements from each of them:
- The ComplexSubset class in Ptolemy 0.x, written by Joe Buck, which borrowed design elements from the cfront and libg++ Complex classes.
- Version 1.0 of the Complex class by Alma services, dated Fri 29-Aug-97, written by Sandy Anderson and Priyantha Jayanetti, and obtained from the Netlib Repository.
- The Complex class in JNL, a Java Numerical Library, dated 1997, by Visual Numerics, Inc. This was used for interface design only, to compare the choice of method names and method templates.
- Matlab, which was used to validate the results in the test suite, and influenced some of the method name choices.
Since:

Ptolemy II 0.2

Version:

$Id$

Author:

Edward A. Lee, Jeff Tsay, Steve Neuendorffer, Adam Cataldo

Pt.AcceptedRating:

Red (cxh)

Pt.ProposedRating:

Yellow (eal)

Field Summary

Fields
Modifier and Type	Field and Description
`static double`	`EPSILON` A small number ( = 1.0e-9).
`static Complex`	`I` A Complex number representing i.
`double`	`imag` The imaginary part.
`static Complex`	`NEGATIVE_INFINITY` A Complex number representing negative infinity, by which we mean that both the real and imaginary parts are equal to Double.NEGATIVE_INFINITY.
`static Complex`	`ONE` A Complex number representing one.
`static Complex`	`POSITIVE_INFINITY` A Complex number representing positive infinity, by which we mean that both the real and imaginary parts are equal to Double.POSITIVE_INFINITY.
`double`	`real` The real part.
`static Complex`	`ZERO` A Complex number representing zero.

Constructor Summary

Constructors
Constructor and Description
`Complex()` Deprecated. Use Complex.ZERO instead.
`Complex(double real)` Construct a Complex with a zero imaginary part.
`Complex(double real, double imag)` Construct a Complex with the specified real and imaginary parts.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`abs(Complex x)` Return the magnitude or absolute value of the specified complex number.
`Complex`	`acos()` Return the principal arc cosine of this complex number.
`static Complex`	`acos(Complex z)` Return the principal arc cosine of the specified complex number.
`Complex`	`acosh()` Return the principal hyperbolic arc cosine of this complex number.
`static Complex`	`acosh(Complex z)` Return the principal hyperbolic arc cosine of the given complex number.
`Complex`	`add(Complex z)` Return the sum of this complex number and the argument z.
`double`	`angle()` Return the angle or argument of this complex number.
`static double`	`angle(Complex z)` Return the angle or argument of this complex number.
`Complex`	`asin()` Return the principal arc sine of this complex number.
`static Complex`	`asin(Complex z)` Return the principal arc sine of the given complex number.
`Complex`	`asinh()` Return the principal hyperbolic arc sine of this complex number.
`static Complex`	`asinh(Complex z)` Return the principal hyperbolic arc sine of the given complex number.
`Complex`	`atan()` Return the principal arc tangent of this complex number.
`static Complex`	`atan(Complex z)` Return the principal arc tangent of the given complex number.
`Complex`	`atanh()` Return the principal hyperbolic arc tangent of this complex number.
`static Complex`	`atanh(Complex z)` Return the principal hyperbolic arc tangent of the given complex number.
`Complex`	`conjugate()` Return the complex conjugate of this complex number.
`static Complex`	`conjugate(Complex z)` Return the complex conjugate of the specified complex number.
`static Complex`	`conjugate(double z)` Return the complex conjugate of the specified real number, which is just the real number itself.
`Complex`	`cos()` Return the cosine of this complex number.
`static Complex`	`cos(Complex z)` Return the cosine of the given complex number.
`Complex`	`cosh()` Return the hyperbolic cosine of this complex number.
`static Complex`	`cosh(Complex z)` Return the hyperbolic cosine of the given complex number.
`Complex`	`cot()` Return the cotangent of this complex number.
`static Complex`	`cot(Complex z)` Return the cotangent of the given complex number.
`Complex`	`csc()` Return the cosecant of this complex number.
`static Complex`	`csc(Complex z)` Return the cosecant of the given complex number.
`Complex`	`divide(Complex divisor)` Divide this complex number by the argument, and return the result in a new Complex object.
`boolean`	`equals(java.lang.Object z)` Return true if the real and imaginary parts of this complex number are equal to those of the argument.
`Complex`	`exp()` Return the exponential of this complex number, or e^z, where `z` is this complex number.
`static Complex`	`exp(Complex z)` Return the exponential of the specified complex number, or e^z, where `z` is the argument.
`int`	`hashCode()` Return a hash code value for this Complex.
`static double`	`imag(Complex z)` Return the imaginary part of the specified complex number.
`static double`	`imag(double z)` Return the imaginary part of the specified real number, which is 0.0.
`boolean`	`isCloseTo(Complex z)` Return true if the distance between this complex number and the argument is less than or equal to EPSILON.
`boolean`	`isCloseTo(Complex z, double distance)` Return true if the distance between this complex number and the first argument is less than or equal to the second argument.
`boolean`	`isInfinite()` Return true if either the real or imaginary part is infinite.
`static boolean`	`isInfinite(Complex z)` Return true if either the real or imaginary part of the given complex number is infinite.
`boolean`	`isNaN()` Return true if either the real or imaginary part is NaN.
`static boolean`	`isNaN(Complex z)` Return true if either the real or imaginary part of the given Complex number is NaN.
`Complex`	`log()` Return the natural logarithm of this complex number.
`static Complex`	`log(Complex z)` Return the natural logarithm of the specified complex number.
`double`	`magnitude()` Return the magnitude or absolute value of this complex number.
`static double`	`magnitude(Complex z)` Return the magnitude or absolute value of the given complex number.
`double`	`magnitudeSquared()` Return the square of the magnitude of this complex number.
`static double`	`magnitudeSquared(Complex z)` Return the square of the magnitude of this complex number.
`Complex`	`multiply(Complex w)` Return a new complex number that is formed by multiplying this complex number by the specified complex number.
`Complex`	`negate()` Negate this complex number.
`static Complex`	`polarToComplex(double magnitude, double angle)` Return a new complex number with the specified magnitude and angle.
`Complex`	`pow(Complex y)` Return z^y where z is this complex number and y is the argument, a Complex.
`static Complex`	`pow(Complex z, Complex y)` Return a new complex number with value z ^y where z is the first argument and y is the second argument.
`static Complex`	`pow(Complex z, double y)` Return a new complex number with value z ^y where z is the first argument and y is the second argument.
`Complex`	`pow(double y)` Return a new complex number with value z ^y where z is this complex number and y is the argument, a double.
`static Complex`	`pow(double z, Complex y)` Return a new complex number with value z ^y where z is the first argument and y is the second argument.
`static double`	`real(Complex z)` Return the real part of the specified complex number.
`static double`	`real(double z)` Return the real part of the specified real number, which is the real number itself.
`Complex`	`reciprocal()` Return the reciprocal of this complex number.
`static Complex`	`reciprocal(Complex z)` Return the reciprocal of this complex number.
`static Complex[]`	`roots(Complex z, int n)` Return the nth roots of the given complex number in an array.
`Complex[]`	`roots(int n)` Return the nth roots of this complex number in an array.
`Complex`	`scale(double scalar)` Return a new complex number with value equal to the product of this complex number and the real argument.
`Complex`	`sec()` Return a new complex number with value equal to the secant of this complex number.
`static Complex`	`sec(Complex z)` Return a new complex number with value equal to the secant of the given complex number.
`Complex`	`sin()` Return a new complex number with value equal to the sine of this complex number.
`static Complex`	`sin(Complex z)` Return a new complex number with value equal to the sine of the given complex number.
`Complex`	`sinh()` Return a new complex number with value equal to the hyperbolic sine of this complex number.
`static Complex`	`sinh(Complex z)` Return a new complex number with value equal to the hyperbolic sine of this complex number.
`Complex`	`sqrt()` Return a new complex number with its value equal to the the square root of this complex number.
`static Complex`	`sqrt(Complex z)` Return a new complex number with its value equal to the the square root of the specified complex number.
`Complex`	`subtract(Complex w)` Return a new complex number formed by subtracting the specified complex number from this complex number.
`Complex`	`tan()` Return a new complex number with value equal to the tangent of this complex number.
`static Complex`	`tan(Complex z)` Return a new complex number with value equal to the tangent of the given complex number.
`Complex`	`tanh()` Return a new complex number with value equal to the hyperbolic tangent of this complex number.
`static Complex`	`tanh(Complex z)` Return a new complex number with value equal to the hyperbolic tangent of the given complex number.
`java.lang.String`	`toString()` Return a string representation of this Complex.
`static java.lang.String`	`toString(Complex value)` Return a string representation of the given Complex.

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

- Field Detail
  - real
```
public final double real
```
    The real part. This is a "blank final," which means that it can only be set in the constructor.
  - imag
```
public final double imag
```
    The imaginary part. This is a "blank final," which means that it can only be set in the constructor.
  - EPSILON
```
public static double EPSILON
```
    A small number ( = 1.0e-9). This number is used by algorithms to detect whether a double is close to zero. This value is public so that it can be changed on platforms with different precisions. This variable is not final so that users may set it as necessary.
  - NEGATIVE_INFINITY
```
public static final Complex NEGATIVE_INFINITY
```
    A Complex number representing negative infinity, by which we mean that both the real and imaginary parts are equal to Double.NEGATIVE_INFINITY.
  - POSITIVE_INFINITY
```
public static final Complex POSITIVE_INFINITY
```
    A Complex number representing positive infinity, by which we mean that both the real and imaginary parts are equal to Double.POSITIVE_INFINITY.
  - ZERO
```
public static final Complex ZERO
```
    A Complex number representing zero. Reference this to save memory usage and construction overhead.
  - ONE
```
public static final Complex ONE
```
    A Complex number representing one. Reference this to save memory usage and construction overhead.
  - I
```
public static final Complex I
```
    A Complex number representing i. Reference this to save memory usage and construction overhead.
- Constructor Detail
  - Complex
```
@Deprecated
public Complex()
```
    Deprecated. Use Complex.ZERO instead.
    
    Construct a Complex equal to zero.
  - Complex
```
public Complex(double real)
```
    Construct a Complex with a zero imaginary part.
    
    Parameters:
    
    real - The real part.
  - Complex
```
public Complex(double real,
               double imag)
```
    Construct a Complex with the specified real and imaginary parts.
    
    Parameters:
    
    real - The real part.
    
    imag - The imaginary part.
- Method Detail
  - abs
```
public static double abs(Complex x)
```
    Return the magnitude or absolute value of the specified complex number.
    
    Parameters:
    
    x - The specified number.
    
    Returns:
    
    A non-negative number that is the absolute value of this complex number.
  - acos
```
public final Complex acos()
```
    Return the principal arc cosine of this complex number. This is defined by:
```
   acos(z) = -i * log(z + i*sqrt(1 - z*z))
  
```
    where z is this complex number.
    Returns:
    
    A new complex number with value equal to the arc cosine of the given complex number.
  - acos
```
public static Complex acos(Complex z)
```
    Return the principal arc cosine of the specified complex number. This is defined by:
```
   acos(z) = -i * log(z + i*sqrt(1 - z*z))
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number with value equal to the arc cosine of the given complex number.
  - acosh
```
public final Complex acosh()
```
    Return the principal hyperbolic arc cosine of this complex number. This is defined by:
```
   acosh(z) = log(z + sqrt(z*z - 1))
  
```
    where z is this complex number.
    Returns:
    
    A new complex number with value equal to the principal hyperbolic arc cosine of this complex number.
  - acosh
```
public static Complex acosh(Complex z)
```
    Return the principal hyperbolic arc cosine of the given complex number. This is defined by:
```
   acosh(z) = log(z + sqrt(z*z - 1))
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number with value equal to the principal hyperbolic arc cosine of this complex number.
  - add
```
public final Complex add(Complex z)
```
    Return the sum of this complex number and the argument z.
    
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number equal to the sume of the given complex number and the argument.
  - angle
```
public final double angle()
```
    Return the angle or argument of this complex number.
    
    Returns:
    
    A double in the range -pi to pi.
  - angle
```
public static double angle(Complex z)
```
    Return the angle or argument of this complex number.
    
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A double in the range -pi to pi.
  - asin
```
public final Complex asin()
```
    Return the principal arc sine of this complex number. This is defined by:
```
   asin(z) = -i * log(i*z + sqrt(1 - z*z))
  
```
    where z is this complex number.
    Returns:
    
    A new complex number equal to the principal arc sine of this complex number.
  - asin
```
public static Complex asin(Complex z)
```
    Return the principal arc sine of the given complex number. This is defined by:
```
   asin(z) = -i * log(i*z + sqrt(1 - z*z))
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number equal to the principal arc sine of this complex number.
  - asinh
```
public final Complex asinh()
```
    Return the principal hyperbolic arc sine of this complex number. This is defined by:
```
   asinh(z) = log(z + sqrt(z*z + 1))
  
```
    where z is this complex number.
    Returns:
    
    A new complex number with value equal to the principal hyperbolic arc sine of this complex number.
  - asinh
```
public static Complex asinh(Complex z)
```
    Return the principal hyperbolic arc sine of the given complex number. This is defined by:
```
   asinh(z) = log(z + sqrt(z*z + 1))
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number with value equal to the principal hyperbolic arc sine of this complex number.
  - atan
```
public final Complex atan()
```
    Return the principal arc tangent of this complex number. This is defined by:
```
  atan(z) = -i/2 * log((i-z)/(i+z))
  
```
    where z is this complex number.
    Returns:
    
    a new complex number with value equal to the principal arc tangent of this complex number.
  - atan
```
public static Complex atan(Complex z)
```
    Return the principal arc tangent of the given complex number. This is defined by:
```
  atan(z) = -i/2 * log((i-z)/(i+z))
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    a new complex number with value equal to the principal arc tangent of this complex number.
  - atanh
```
public final Complex atanh()
```
    Return the principal hyperbolic arc tangent of this complex number. This is defined by:
```
   atanh(z) = 1/2 * log((1+z)/(1-z))
  
```
    where z is this complex number.
    Returns:
    
    a new complex number with value equal to the principal hyperbolic arc tangent of this complex number.
  - atanh
```
public static Complex atanh(Complex z)
```
    Return the principal hyperbolic arc tangent of the given complex number. This is defined by:
```
   atanh(z) = 1/2 * log((1+z)/(1-z))
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    a new complex number with value equal to the principal hyperbolic arc tangent of this complex number.
  - conjugate
```
public final Complex conjugate()
```
    Return the complex conjugate of this complex number.
    
    Returns:
    
    A new Complex with value equal to the complex conjugate of of this complex number.
  - conjugate
```
public static final Complex conjugate(Complex z)
```
    Return the complex conjugate of the specified complex number.
    
    Parameters:
    
    z - The specified complex number.
    
    Returns:
    
    A new Complex with value equal to the complex conjugate of of the specified complex number.
  - conjugate
```
public static final Complex conjugate(double z)
```
    Return the complex conjugate of the specified real number, which is just the real number itself. This method is provided for completeness in the expression language.
    
    Parameters:
    
    z - The specified real number.
    
    Returns:
    
    The number provided as an argument, but converted to complex.
  - cos
```
public final Complex cos()
```
    Return the cosine of this complex number. This is defined by:
```
  cos(z) = (exp(i*z) + exp(-i*z))/2
  
```
    where z is this complex number.
    Returns:
    
    a new complex number with value equal to the cosine of this complex number.
  - cos
```
public static Complex cos(Complex z)
```
    Return the cosine of the given complex number. This is defined by:
```
  cos(z) = (exp(i*z) + exp(-i*z))/2
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    a new complex number with value equal to the cosine of this complex number.
  - cosh
```
public final Complex cosh()
```
    Return the hyperbolic cosine of this complex number. This is defined by:
```
  cosh(z) = (exp(z) + exp(-z))/2
  
```
    where z is this complex number.
    Returns:
    
    A new complex number with value equal to the hyperbolic cosine of this complex number.
  - cosh
```
public static Complex cosh(Complex z)
```
    Return the hyperbolic cosine of the given complex number. This is defined by:
```
  cosh(z) = (exp(z) + exp(-z))/2
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number with value equal to the hyperbolic cosine of this complex number.
  - cot
```
public final Complex cot()
```
    Return the cotangent of this complex number. This is simply:
```
  cot(z) = 1/tan(z)
  
```
    where z is this complex number.
    Returns:
    
    A new complex number with value equal to the cotangent of this complex number.
  - cot
```
public static Complex cot(Complex z)
```
    Return the cotangent of the given complex number. This is simply:
```
  cot(z) = 1/tan(z)
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number with value equal to the cotangent of this complex number.
  - csc
```
public Complex csc()
```
    Return the cosecant of this complex number. This is simply:
```
  csc(z) = 1/sin(z)
  
```
    where z is this complex number.
    Returns:
    
    A new complex number with value equal to the cosecant of this complex number.
  - csc
```
public static Complex csc(Complex z)
```
    Return the cosecant of the given complex number. This is simply:
```
  csc(z) = 1/sin(z)
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number with value equal to the cosecant of this complex number.
  - divide
```
public final Complex divide(Complex divisor)
```
    Divide this complex number by the argument, and return the result in a new Complex object.
    
    Parameters:
    
    divisor - The denominator in the division.
    
    Returns:
    
    A new complex number equal to this complex number divided by the argument.
  - equals
```
public final boolean equals(java.lang.Object z)
```
    Return true if the real and imaginary parts of this complex number are equal to those of the argument.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    z - The argument to which this number is being compared.
    
    Returns:
    
    True if the real and imaginary parts are equal.
  - exp
```
public final Complex exp()
```
    Return the exponential of this complex number, or e^z, where z is this complex number.
    
    Returns:
    
    A new complex number with value equal to the exponential of this complex number.
  - exp
```
public static Complex exp(Complex z)
```
    Return the exponential of the specified complex number, or e^z, where z is the argument.
    
    Parameters:
    
    z - A complex exponent.
    
    Returns:
    
    A new complex number with value equal to the exponential of this complex number.
  - hashCode
```
public int hashCode()
```
    Return a hash code value for this Complex. This method returns the bitwise xor of the hashcode of the real and imaginary parts.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    A hash code value for this Complex.
  - imag
```
public static double imag(Complex z)
```
    Return the imaginary part of the specified complex number.
    
    Parameters:
    
    z - The complex number.
    
    Returns:
    
    The imaginary part of the argument.
  - imag
```
public static double imag(double z)
```
    Return the imaginary part of the specified real number, which is 0.0.
    
    Parameters:
    
    z - The complex number.
    
    Returns:
    
    0.0.
  - isCloseTo
```
public final boolean isCloseTo(Complex z)
```
    Return true if the distance between this complex number and the argument is less than or equal to EPSILON.
    
    Parameters:
    
    z - The number to compare against.
    
    Returns:
    
    True if the distance to the argument is less than or equal to EPSILON.
    
    See Also:
    
    EPSILON
  - isCloseTo
```
public final boolean isCloseTo(Complex z,
                               double distance)
```
    Return true if the distance between this complex number and the first argument is less than or equal to the second argument. If the distance argument is negative, return false.
    
    Parameters:
    
    z - The number to compare against.
    
    distance - The distance criterion.
    
    Returns:
    
    True if the distance to the first argument is less than or equal to the second argument.
  - isInfinite
```
public final boolean isInfinite()
```
    Return true if either the real or imaginary part is infinite. This is determined by the isInfinite() method of the java.lang.Double class.
    
    Returns:
    
    True if this is infinite.
  - isInfinite
```
public static boolean isInfinite(Complex z)
```
    Return true if either the real or imaginary part of the given complex number is infinite. This is determined by the isInfinite() method of the java.lang.Double class.
    
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    True if this is infinite.
  - isNaN
```
public final boolean isNaN()
```
    Return true if either the real or imaginary part is NaN. NaN means "not a number," per the IEEE floating point standard. This is determined by the isNaN() method of the java.lang.Double class.
    
    Returns:
    
    True if this is NaN.
  - isNaN
```
public static boolean isNaN(Complex z)
```
    Return true if either the real or imaginary part of the given Complex number is NaN. NaN means "not a number," per the IEEE floating point standard. This is determined by the isNaN() method of the java.lang.Double class.
    
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    True if this is NaN.
  - log
```
public final Complex log()
```
    Return the natural logarithm of this complex number. The principal value is returned, which is
```
  log(z) = log(abs(z)) + i * angle(z)
  
```
    where z is this complex number, abs(z) is its magnitude, and angle(z) is its angle.
    Returns:
    
    A new complex number with value equal to the natural logarithm of this complex number.
  - log
```
public static Complex log(Complex z)
```
    Return the natural logarithm of the specified complex number. The principal value is returned, which is
```
  log(z) = log(abs(z)) + i * angle(z)
  
```
    where z is this complex number, abs(z) is its magnitude, and angle(z) is its angle.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number with value equal to the natural logarithm of this complex number.
  - magnitude
```
public final double magnitude()
```
    Return the magnitude or absolute value of this complex number.
    
    Returns:
    
    A non-negative number that is the absolute value of this complex number.
  - magnitude
```
public static double magnitude(Complex z)
```
    Return the magnitude or absolute value of the given complex number.
    
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A non-negative number that is the absolute value of this complex number.
  - magnitudeSquared
```
public double magnitudeSquared()
```
    Return the square of the magnitude of this complex number. This is provided for efficiency, since it is considerably easier to compute than the magnitude (which is the square root of this result).
    
    Returns:
    
    A non-negative number which is the magnitude of this complex number.
  - magnitudeSquared
```
public static double magnitudeSquared(Complex z)
```
    Return the square of the magnitude of this complex number. This is provided for efficiency, since it is considerably easier to compute than the magnitude (which is the square root of this result).
    
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A non-negative number which is the magnitude of this complex number.
  - multiply
```
public Complex multiply(Complex w)
```
    Return a new complex number that is formed by multiplying this complex number by the specified complex number.
    
    Parameters:
    
    w - The specified complex number.
    
    Returns:
    
    A new complex number which is the product of this complex number and the specified complex number.
    
    See Also:
    
    scale(double)
  - negate
```
public final Complex negate()
```
    Negate this complex number.
    
    Returns:
    
    A new complex number that is formed by taking the negatives of both the real and imaginary parts of this complex number.
  - polarToComplex
```
public static Complex polarToComplex(double magnitude,
                                     double angle)
```
    Return a new complex number with the specified magnitude and angle.
    
    Parameters:
    
    magnitude - The magnitude.
    
    angle - The angle.
    
    Returns:
    
    A new complex number with the specified magnitude and angle.
  - pow
```
public Complex pow(double y)
```
    Return a new complex number with value z ^y where z is this complex number and y is the argument, a double.
    
    Parameters:
    
    y - The exponent, which is a double.
    
    Returns:
    
    A new complex number that with value z ^y.
  - pow
```
public static Complex pow(Complex z,
                          double y)
```
    Return a new complex number with value z ^y where z is the first argument and y is the second argument.
    
    Parameters:
    
    z - The number to be raised to a power.
    
    y - The exponent.
    
    Returns:
    
    A new complex number that with value z ^y.
  - pow
```
public final Complex pow(Complex y)
```
    Return z^y where z is this complex number and y is the argument, a Complex.
    
    Parameters:
    
    y - The exponent, which is a complex number.
    
    Returns:
    
    A new complex number equal to z^y.
  - pow
```
public static Complex pow(Complex z,
                          Complex y)
```
    Return a new complex number with value z ^y where z is the first argument and y is the second argument.
    
    Parameters:
    
    z - The number to be raised to a power.
    
    y - The exponent.
    
    Returns:
    
    A new complex number that with value z ^y.
  - pow
```
public static Complex pow(double z,
                          Complex y)
```
    Return a new complex number with value z ^y where z is the first argument and y is the second argument.
    
    Parameters:
    
    z - The number to be raised to a power.
    
    y - The exponent.
    
    Returns:
    
    A new complex number that with value z ^y.
  - real
```
public static double real(Complex z)
```
    Return the real part of the specified complex number.
    
    Parameters:
    
    z - The complex number.
    
    Returns:
    
    The real part of the argument.
  - real
```
public static double real(double z)
```
    Return the real part of the specified real number, which is the real number itself.
    
    Parameters:
    
    z - The complex number.
    
    Returns:
    
    The argument.
  - reciprocal
```
public final Complex reciprocal()
```
    Return the reciprocal of this complex number. The result 1/a is given by (a*)/|a|^2.
    
    Returns:
    
    A new complex number that is the reciprocal of this one.
  - reciprocal
```
public static Complex reciprocal(Complex z)
```
    Return the reciprocal of this complex number. The result 1/a is given by (a*)/|a|^2.
    
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number that is the reciprocal of this one.
  - roots
```
public final Complex[] roots(int n)
```
    Return the nth roots of this complex number in an array. There are n of them, computed by : r^1/n(cos((theta + 2kPI) / n + i sin((theta + 2kPI)/n) where k is the index of the returned array. If n is not greater than or equal to one, throw a IllegalArgumentException.
    
    Parameters:
    
    n - An integer that must be greater than or equal to one.
    
    Returns:
    
    An array of Complex numbers, containing the n roots.
  - roots
```
public static Complex[] roots(Complex z,
                              int n)
```
    Return the nth roots of the given complex number in an array. There are n of them, computed by : r^1/n(cos((theta + 2kPI) / n + i sin((theta + 2kPI)/n) where k is the index of the returned array. If n is not greater than or equal to one, throw a IllegalArgumentException.
    
    Parameters:
    
    z - A complex number.
    
    n - An integer that must be greater than or equal to one.
    
    Returns:
    
    An array of Complex numbers, containing the n roots.
  - scale
```
public final Complex scale(double scalar)
```
    Return a new complex number with value equal to the product of this complex number and the real argument.
    
    Parameters:
    
    scalar - A real number.
    
    Returns:
    
    A new complex number with value equal to the product of this complex number and the real argument.
    
    See Also:
    
    multiply(ptolemy.math.Complex)
  - sec
```
public Complex sec()
```
    Return a new complex number with value equal to the secant of this complex number. This is simply:
```
  sec(z) = 1/cos(z)
  
```
    where z is this complex number.
    Returns:
    
    A new complex number equal to the secant of this complex number.
  - sec
```
public static Complex sec(Complex z)
```
    Return a new complex number with value equal to the secant of the given complex number. This is simply:
```
  sec(z) = 1/cos(z)
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number equal to the secant of this complex number.
  - sin
```
public final Complex sin()
```
    Return a new complex number with value equal to the sine of this complex number. This is defined by:
```
  sin(z) = (exp(i*z) - exp(-i*z))/(2*i)
  
```
    where z is this complex number.
    Returns:
    
    A new complex number equal to the sine of this complex number.
  - sin
```
public static Complex sin(Complex z)
```
    Return a new complex number with value equal to the sine of the given complex number. This is defined by:
```
  sin(z) = (exp(i*z) - exp(-i*z))/(2*i)
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number equal to the sine of this complex number.
  - sinh
```
public final Complex sinh()
```
    Return a new complex number with value equal to the hyperbolic sine of this complex number. This is defined by:
```
  sinh(z) = (exp(z) - exp(-z))/2
  
```
    where z is this complex number.
    Returns:
    
    A new complex number equal to the hyperbolic sine of this complex number.
  - sinh
```
public static Complex sinh(Complex z)
```
    Return a new complex number with value equal to the hyperbolic sine of this complex number. This is defined by:
```
  sinh(z) = (exp(z) - exp(-z))/2
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number equal to the hyperbolic sine of this complex number.
  - sqrt
```
public final Complex sqrt()
```
    Return a new complex number with its value equal to the the square root of this complex number. The square root is defined to be:
```
  sqrt(z) = sqrt(mag(z))*(cos(angle(z)/2) + i * sin(angle(z)/2) )
  
```
    where z is this complex number.
    Returns:
    
    A new complex number equal to the square root of this complex number.
  - sqrt
```
public static Complex sqrt(Complex z)
```
    Return a new complex number with its value equal to the the square root of the specified complex number. The square root is defined to be:
```
  sqrt(z) = sqrt(mag(z))*(cos(angle(z)/2) + i * sin(angle(z)/2) )
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number equal to the square root of this complex number.
  - subtract
```
public final Complex subtract(Complex w)
```
    Return a new complex number formed by subtracting the specified complex number from this complex number.
    
    Parameters:
    
    w - The number that is being subtracted.
    
    Returns:
    
    A new complex number formed by subtracting the specified complex number from this complex number.
  - tan
```
public final Complex tan()
```
    Return a new complex number with value equal to the tangent of this complex number. This is defined by:
```
  tan(z) = sin(z)/cos(z)
  
```
    where z is this complex number.
    Returns:
    
    A new complex number equal to sin(z)/cos(z).
  - tan
```
public static Complex tan(Complex z)
```
    Return a new complex number with value equal to the tangent of the given complex number. This is defined by:
```
  tan(z) = sin(z)/cos(z)
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number equal to sin(z)/cos(z).
  - tanh
```
public final Complex tanh()
```
    Return a new complex number with value equal to the hyperbolic tangent of this complex number. This is defined by:
```
  tanh(z) = sinh(z)/cosh(z)
  
```
    where z is this complex number.
    Returns:
    
    A new complex number equal to sinh(z)/cosh(z).
  - tanh
```
public static Complex tanh(Complex z)
```
    Return a new complex number with value equal to the hyperbolic tangent of the given complex number. This is defined by:
```
  tanh(z) = sinh(z)/cosh(z)
  
```
    where z is this complex number.
    Parameters:
    
    z - A complex number.
    
    Returns:
    
    A new complex number equal to sinh(z)/cosh(z).
  - toString
```
public final java.lang.String toString()
```
    Return a string representation of this Complex.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    A string of the form "x + yi".
  - toString
```
public static java.lang.String toString(Complex value)
```
    Return a string representation of the given Complex.
    
    Parameters:
    
    value - The given value.
    
    Returns:
    
    A string of the form "x + yi".

Class Complex

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

real

imag

EPSILON

NEGATIVE_INFINITY

POSITIVE_INFINITY

ZERO

ONE

I

Constructor Detail

Complex

Complex

Complex

Method Detail

abs

acos

acos

acosh

acosh

add

angle

angle

asin

asin

asinh

asinh

atan

atan

atanh

atanh

conjugate

conjugate

conjugate

cos

cos

cosh

cosh

cot

cot

csc

csc

divide

equals

exp

exp

hashCode

imag

imag

isCloseTo

isCloseTo

isInfinite

isInfinite

isNaN

isNaN

log

log

magnitude

magnitude

magnitudeSquared

magnitudeSquared

multiply

negate

polarToComplex

pow

pow

pow

pow

pow

real

real

reciprocal

reciprocal

roots

roots

scale