: Class Complex

ORG.netlib.math.complex
Class Complex

java.lang.Object
  |
  +--ORG.netlib.math.complex.Complex

All Implemented Interfaces:: java.lang.Cloneable, java.io.Serializable

public class Complex
extends java.lang.Object
implements java.lang.Cloneable, java.io.Serializable

Version:: 1.0.1
Last change: ALM 23 Mar 2001 8:56 pm

A Java class for performing complex number arithmetic to double precision.

Make yours a Java enabled browser and OS!

This applet has been adapted
from a Vector Visualization applet by Vladimir Sorokin.

Author:

Sandy Anderson, Priyantha Jayanetti

  Copyright (c) 1997 - 2001, Alexander Anderson.

  This  program is free software; you can redistribute it and/or modify
  it under the terms of the GNU General Public License as published  by
  the Free Software Foundation; either version 2 of the License, or (at
  your option) any later version.

  This program is distributed in the hope that it will be  useful,  but
  WITHOUT   ANY   WARRANTY;   without  even  the  implied  warranty  of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR  PURPOSE.   See  the  GNU
  General Public License for more details.

  You  should  have  received  a copy of the GNU General Public License
  along  with  this  program;  if  not,  write  to  the  Free  Software
  Foundation,  Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307
  USA.

The latest version of this Complex class is available from the Netlib Repository.

Here's an example of the style the class permits:

         import  ORG.netlib.math.complex.Complex;

         public class Test {

             public boolean isInMandelbrot (Complex c, int maxIter) {
                 Complex z= new Complex(0, 0);

                 for (int i= 0; i < maxIter; i++) {
                     z= z.mul(z).add(c);
                     if (z.abs() > 2) return false;
                 }

                 return true;
             }

         }

This class was developed by Sandy Anderson at the School of Electronic Engineering, Middlesex University, UK, and Priyantha Jayanetti at The Power Systems Program, the University of Maine, USA.

And many, many thanks to Mr. Daniel Hirsch, for his constant advice on the mathematics, his exasperating ability to uncover bugs blindfold, and for his persistent badgering over the exact wording of this documentation.

For instance, he starts to growl like a badger if you say "infinite set".

"Grrr...What's that mean? Countably infinite?"

You think for a while.

"Grrr..."

"Yes."

"Ah! Then you mean infinitely many."

Field Summary

static java.lang.String AUTHOR


static java.lang.String DATE


static Complex i
          A constant representing i, the famous square root of -1.

static java.lang.String REMARK


protected static double TWO_PI
          Twice PI radians is the same thing as 360 degrees.

static java.lang.String VERSION


Constructor Summary

Complex()
          Constructs a Complex representing the number zero.

Complex(Complex z)
          Constructs a separate new Complex from an existing Complex.

Complex(double re)
          Constructs a Complex representing a real number.

Complex(double re, double im)
          Constructs a Complex from real and imaginary parts.

Method Summary

double abs()
          Returns the magnitude of a Complex number.

Complex acos()
          Returns the principal arc cosine of a Complex number.

Complex acosh()
          Returns the principal inverse hyperbolic cosine of a Complex number.

Complex add(Complex z)
          To perform z1 + z2, you write z1.add(z2) .

double arg()
          Returns the principal angle of a Complex number, in radians, measured counter-clockwise from the real axis.

Complex asin()
          Returns the principal arc sine of a Complex number.

Complex asinh()
          Returns the principal inverse hyperbolic sine of a Complex number.

Complex atan()
          Returns the principal arc tangent of a Complex number.

Complex atanh()
          Returns the principal inverse hyperbolic tangent of a Complex number.

static Complex cart(double re, double im)
          Returns a Complex from real and imaginary parts.

java.lang.Object clone()
          Overrides the Cloneable interface.

Complex conj()
          Returns the Complex "conjugate".

Complex cos()
          Returns the cosine of a Complex number.

Complex cosec()
          Returns the cosecant of a Complex number.

Complex cosh()
          Returns the hyperbolic cosine of a Complex number.

Complex cot()
          Returns the cotangent of a Complex number.

Complex div(Complex z)
          To perform z1 / z2, you write z1.div(z2) .

boolean equals(Complex z, double tolerance)
          Decides if two Complex numbers are "sufficiently" alike to be considered equal.

Complex exp()
          Returns the number e "raised to" a Complex power.

double im()
          Extracts the imaginary part of a Complex as a double.

boolean isInfinite()
          Returns true if either the real or imaginary component of this Complex is an infinite value.

boolean isNaN()
          Returns true if either the real or imaginary component of this Complex is a Not-a-Number (NaN) value.

Complex log()
          Returns the principal natural logarithm of a Complex number.

static void main(java.lang.String[] args)
          Useful for checking up on the exact version.

Complex mul(Complex z)
          To perform z1 * z2, you write z1.mul(z2) .

Complex neg()
          Returns the "negative" of a Complex number.

double norm()
          Returns the square of the "length" of a Complex number.

static Complex polar(double r, double theta)
          Returns a Complex from a size and direction.

Complex pow(Complex exponent)
          Returns this Complex raised to the power of a Complex exponent.

static Complex pow(Complex base, Complex exponent)
          Returns the Complex base raised to the power of the Complex exponent.

static Complex pow(Complex base, double exponent)
          Returns the Complex base raised to the power of the exponent.

static Complex pow(double base, Complex exponent)
          Returns the base raised to the power of the Complex exponent.

double re()
          Extracts the real part of a Complex as a double.

static Complex real(double real)
          Returns a Complex representing a real number.

Complex scale(double scalar)
          Returns the Complex scaled by a real number.

Complex sec()
          Returns the secant of a Complex number.

Complex sin()
          Returns the sine of a Complex number.

Complex sinh()
          Returns the hyperbolic sine of a Complex number.

Complex sqrt()
          Returns a Complex representing one of the two square roots.

Complex sub(Complex z)
          To perform z1 - z2, you write z1.sub(z2) .

Complex tan()
          Returns the tangent of a Complex number.

Complex tanh()
          Returns the hyperbolic tangent of a Complex number.

java.lang.String toString()
          Converts a Complex into a String of the form (a + bi).

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

AUTHOR

public static final java.lang.String AUTHOR

DATE

public static final java.lang.String DATE

i

public static final Complex i

A constant representing i, the famous square root of -1.

The other square root of -1 is - i.

REMARK

public static final java.lang.String REMARK

TWO_PI

protected static final double TWO_PI

Twice PI radians is the same thing as 360 degrees.

VERSION

public static final java.lang.String VERSION

Constructor Detail

Complex

public Complex()

Constructs a Complex representing the number zero.

Complex

public Complex(Complex z)

Constructs a separate new Complex from an existing Complex.

Parameters:: z - A Complex number

Complex

public Complex(double re)

Constructs a Complex representing a real number.

Parameters:: re - The real number
See Also:: real(double)

Complex

public Complex(double re,
               double im)

Constructs a Complex from real and imaginary parts.

Note:

All methods in class Complex which deliver a Complex are written such that no intermediate Complex objects get generated. This means that you can easily anticipate the likely effects on garbage collection caused by your own coding.

Parameters:: re - Real part; im - Imaginary part
See Also:: cart(double, double), polar(double, double)

Method Detail

abs

public double abs()

Returns the magnitude of a Complex number.

     abs(z)  =  sqrt(norm(z))

In other words, it's Pythagorean distance from the origin (0 + 0i, or zero).

The magnitude is also referred to as the "modulus" or "length".

Always non-negative.

Returns:: The magnitude (or "length")
See Also:: arg(), polar(double, double), norm()

acos

public Complex acos()

Returns the principal arc cosine of a Complex number.

     acos(z)  =  -i * log( z + i * sqrt(1 - z*z) )

There are infinitely many solutions, besides the principal solution. If A is the principal solution of acos(z), the others are of the form:

     2*k*PI +/- A

where k is any integer.

Returns:: Principal Complex arc cosine
See Also:: cos(), cosh()

acosh

public Complex acosh()

Returns the principal inverse hyperbolic cosine of a Complex number.

     acosh(z)  =  log(z + sqrt(z*z - 1))

There are infinitely many solutions, besides the principal solution. If A is the principal solution of acosh(z), the others are of the form:

     2*k*PI*i +/- A

where k is any integer.

Returns:: Principal Complex inverse hyperbolic cosine
See Also:: cosh()

add

public Complex add(Complex z)

To perform z1 + z2, you write z1.add(z2) .

     (a + i*b) + (c + i*d)  =  ((a+c) + i*(b+d))

arg

public double arg()

Returns the principal angle of a Complex number, in radians, measured counter-clockwise from the real axis. (Think of the reals as the x-axis, and the imaginaries as the y-axis.)

There are infinitely many solutions, besides the principal solution. If A is the principal solution of arg(z), the others are of the form:

     A + 2*k*PI

where k is any integer.

arg() always returns a double between -PI and +PI.

Note:

2*PI radians is the same as 360 degrees.

Domain Restrictions:

There are no restrictions: the class defines arg(0) to be 0

Returns:: Principal angle (in radians)
See Also:: abs(), polar(double, double)

asin

public Complex asin()

Returns the principal arc sine of a Complex number.

     asin(z)  =  -i * log(i*z + sqrt(1 - z*z))

There are infinitely many solutions, besides the principal solution. If A is the principal solution of asin(z), the others are of the form:

     k*PI + (-1)^k  * A

where k is any integer.

Returns:: Principal Complex arc sine
See Also:: sin(), sinh()

asinh

public Complex asinh()

Returns the principal inverse hyperbolic sine of a Complex number.

     asinh(z)  =  log(z + sqrt(z*z + 1))

There are infinitely many solutions, besides the principal solution. If A is the principal solution of asinh(z), the others are of the form:

     k*PI*i + (-1)^k  * A

where k is any integer.

Returns:: Principal Complex inverse hyperbolic sine
See Also:: sinh()

atan

public Complex atan()

Returns the principal arc tangent of a Complex number.

     atan(z)  =  -i/2 * log( (i-z)/(i+z) )

There are infinitely many solutions, besides the principal solution. If A is the principal solution of atan(z), the others are of the form:

     A + k*PI

where k is any integer.

Domain Restrictions:

atan(z) is undefined for z = + i or z = - i

Returns:: Principal Complex arc tangent
See Also:: tan(), tanh()

atanh

public Complex atanh()

Returns the principal inverse hyperbolic tangent of a Complex number.

     atanh(z)  =  1/2 * log( (1+z)/(1-z) )

There are infinitely many solutions, besides the principal solution. If A is the principal solution of atanh(z), the others are of the form:

     A + k*PI*i

where k is any integer.

Domain Restrictions:

atanh(z) is undefined for z = + 1 or z = - 1

Returns:: Principal Complex inverse hyperbolic tangent
See Also:: tanh()

cart

public static Complex cart(double re,
                           double im)

Returns a Complex from real and imaginary parts.

Parameters:: re - Real part; im - Imaginary part
Returns:: Complex from Cartesian coordinates
See Also:: re(), im(), polar(double, double), toString()

clone

public java.lang.Object clone()

Overrides the Cloneable interface.

Standard override; no change in semantics.

The following Java code example illustrates how to clone, or copy, a Complex number:

     Complex z1 =  new Complex(0, 1);
     Complex z2 =  (Complex) z1.clone();

Overrides:: clone in class java.lang.Object

Returns:: An Object that is a copy of this Complex object.
See Also:: Cloneable, Object.clone()

conj

public Complex conj()

Returns the Complex "conjugate".

     conj(x + i*y)  =  x - i*y

The conjugate appears "flipped" across the real axis.

Returns:: The Complex conjugate

cos

public Complex cos()

Returns the cosine of a Complex number.

     cos(z)  =  ( exp(i*z) + exp(-i*z) ) / 2

Returns:: The Complex cosine
See Also:: acos(), cosh(), sec(), sin(), tan()

cosec

public Complex cosec()

Returns the cosecant of a Complex number.

     cosec(z)  =  1 / sin(z)

Domain Restrictions:

cosec(z) is undefined whenever z = k * PI
where k is any integer

Returns:: The Complex cosecant
See Also:: sin(), sec(), cot()

cosh

public Complex cosh()

Returns the hyperbolic cosine of a Complex number.

     cosh(z)  =  ( exp(z) + exp(-z) ) / 2

Returns:: The Complex hyperbolic cosine
See Also:: cos(), acosh()

cot

public Complex cot()

Returns the cotangent of a Complex number.

     cot(z)  =  1 / tan(z)

Domain Restrictions:

cot(z) is undefined whenever z = k * PI
where k is any integer

Returns:: The Complex cotangent
See Also:: tan(), cosec(), sec()

div

public Complex div(Complex z)

To perform z1 / z2, you write z1.div(z2) .

     (a + i*b) / (c + i*d)  =  ( (a*c) + (b*d) + i*((b*c) - (a*d)) ) / norm(c + i*d)

Take care not to divide by zero!

Note:

Complex arithmetic in Java never causes exceptions. You have to deliberately check for overflow, division by zero, and so on, for yourself.

Domain Restrictions:

z1/z2 is undefined if z2 = 0

See Also:: scale(double)

equals

public boolean equals(Complex z,
                      double tolerance)

Decides if two Complex numbers are "sufficiently" alike to be considered equal.

tolerance is the maximum magnitude of the difference between them before they are considered not equal.

Checking for equality between two real numbers on computer hardware is a tricky business. Try

    System.out.println((1.0/3.0 * 3.0));

and you'll see the nature of the problem! It's just as tricky with Complex numbers.

Realize that because of these complications, it's possible to find that the magnitude of one Complex number a is less than another, b, and yet a.equals(b, myTolerance) returns true. Be aware!

Parameters:: z - The Complex to compare with; tolerance - The tolerance for equality
Returns:: true, or false

exp

public Complex exp()

Returns the number e "raised to" a Complex power.

     exp(x + i*y)  =  exp(x) * ( cos(y) + i * sin(y) )

Note:

The value of e, a transcendental number, is roughly 2.71828182846...
Also, the following is quietly amazing:
e^PI*i = - 1

Returns:: e "raised to the power of" this Complex
See Also:: log(), pow(double, Complex)

im

public double im()

Extracts the imaginary part of a Complex as a double.

     im(x + i*y)  =  y

Returns:: The imaginary part
See Also:: re(), cart(double, double)

isInfinite

public boolean isInfinite()

Returns true if either the real or imaginary component of this Complex is an infinite value.

Returns:: true if either component of the Complex object is infinite; false, otherwise.

isNaN

public boolean isNaN()

Returns true if either the real or imaginary component of this Complex is a Not-a-Number (NaN) value.

Returns:: true if either component of the Complex object is NaN; false, otherwise.

log

public Complex log()

Returns the principal natural logarithm of a Complex number.

     log(z)  =  log(abs(z)) + i * arg(z)

There are infinitely many solutions, besides the principal solution. If L is the principal solution of log(z), the others are of the form:

     L + (2*k*PI)*i

where k is any integer.

Returns:: Principal Complex natural logarithm
See Also:: exp()

main

public static void main(java.lang.String[] args)

Useful for checking up on the exact version.

mul

public Complex mul(Complex z)

To perform z1 * z2, you write z1.mul(z2) .

     (a + i*b) * (c + i*d)  =  ( (a*c) - (b*d) + i*((a*d) + (b*c)) )

See Also:: scale(double)

neg

public Complex neg()

Returns the "negative" of a Complex number.

     neg(a + i*b)  =  -a - i*b

The magnitude of the negative is the same, but the angle is flipped through PI (or 180 degrees).

Returns:: Negative of the Complex
See Also:: scale(double)

norm

public double norm()

Returns the square of the "length" of a Complex number.

     norm(x + i*y)  =  x*x + y*y

Always non-negative.

Returns:: The norm
See Also:: abs()

polar

public static Complex polar(double r,
                            double theta)

Returns a Complex from a size and direction.

Parameters:: r - Size; theta - Direction (in radians)
Returns:: Complex from Polar coordinates
See Also:: abs(), arg(), cart(double, double)

pow

public Complex pow(Complex exponent)

Returns this Complex raised to the power of a Complex exponent.

Parameters:: exponent - The exponent "by which to raise"
Returns:: this Complex "raised to the power of" the exponent
See Also:: pow(Complex, Complex)

pow

public static Complex pow(Complex base,
                          Complex exponent)

Returns the Complex base raised to the power of the Complex exponent.

Parameters:: base - The base "to raise"; exponent - The exponent "by which to raise"
Returns:: base "raised to the power of" exponent
See Also:: pow(Complex, double), pow(Complex)

pow

public static Complex pow(Complex base,
                          double exponent)

Returns the Complex base raised to the power of the exponent.

Parameters:: base - The base "to raise"; exponent - The exponent "by which to raise"
Returns:: base "raised to the power of" exponent
See Also:: pow(double, Complex)

pow

public static Complex pow(double base,
                          Complex exponent)

Returns the base raised to the power of the Complex exponent.

Parameters:: base - The base "to raise"; exponent - The exponent "by which to raise"
Returns:: base "raised to the power of" exponent
See Also:: pow(Complex, Complex), exp()

re

public double re()

Extracts the real part of a Complex as a double.

     re(x + i*y)  =  x

Returns:: The real part
See Also:: im(), cart(double, double), real(double)

real

public static Complex real(double real)

Returns a Complex representing a real number.

Parameters:: real - The real number
Returns:: Complex representation of the real
See Also:: re(), cart(double, double)

scale

public Complex scale(double scalar)

Returns the Complex scaled by a real number.

     scale((x + i*y), s)  =  (x*s + i*y*s)

Scaling by the real number 2.0, doubles the magnitude, but leaves the arg() unchanged. Scaling by -1.0 keeps the magnitude the same, but flips the arg() by PI (180 degrees).

Parameters:: scalar - A real number scale factor
Returns:: Complex scaled by a real number
See Also:: mul(Complex), div(Complex), neg()

sec

public Complex sec()

Returns the secant of a Complex number.

     sec(z)  =  1 / cos(z)

Domain Restrictions:

sec(z) is undefined whenever z = (k + 1/2) * PI
where k is any integer

Returns:: The Complex secant
See Also:: cos(), cosec(), cot()

sin

public Complex sin()

Returns the sine of a Complex number.

     sin(z)  =  ( exp(i*z) - exp(-i*z) ) / (2*i)

Returns:: The Complex sine
See Also:: asin(), sinh(), cosec(), cos(), tan()

sinh

public Complex sinh()

Returns the hyperbolic sine of a Complex number.

     sinh(z)  =  ( exp(z) - exp(-z) ) / 2

Returns:: The Complex hyperbolic sine
See Also:: sin(), asinh()

sqrt

public Complex sqrt()

Returns a Complex representing one of the two square roots.

     sqrt(z)  =  sqrt(abs(z)) * ( cos(arg(z)/2) + i * sin(arg(z)/2) )

For any complex number z, sqrt(z) will return the complex root whose arg is arg(z)/2.

Note:

There are always two square roots for each Complex number, except for 0 + 0i, or zero. The other root is the neg() of the first one. Just as the two roots of 4 are 2 and -2, the two roots of -1 are i and - i.

Returns:: The square root whose arg is arg(z)/2.
See Also:: pow(Complex, double)

sub

public Complex sub(Complex z)

To perform z1 - z2, you write z1.sub(z2) .

     (a + i*b) - (c + i*d)  =  ((a-c) + i*(b-d))

tan

public Complex tan()

Returns the tangent of a Complex number.

     tan(z)  =  sin(z) / cos(z)

Domain Restrictions:

tan(z) is undefined whenever z = (k + 1/2) * PI
where k is any integer

Returns:: The Complex tangent
See Also:: atan(), tanh(), cot(), sin(), cos()

tanh

public Complex tanh()

Returns the hyperbolic tangent of a Complex number.

     tanh(z)  =  sinh(z) / cosh(z)

Returns:: The Complex hyperbolic tangent
See Also:: tan(), atanh()

toString

public java.lang.String toString()

Converts a Complex into a String of the form (a + bi).

This enables a Complex to be easily printed. For example, if z was 2 - 5i, then

     System.out.println("z = " + z);

would print something like

     z = (2.0 - 5.0i)

Overrides:: toString in class java.lang.Object

Returns:: String containing the cartesian coordinate representation
See Also:: cart(double, double)

Field Summary
`static java.lang.String`	`AUTHOR`
`static java.lang.String`	`DATE`
`static Complex`	`i` A constant representing i, the famous square root of -1.
`static java.lang.String`	`REMARK`
`protected static double`	`TWO_PI` Twice `PI` radians is the same thing as 360 degrees.
`static java.lang.String`	`VERSION`

Constructor Summary
`Complex()` Constructs a `Complex` representing the number zero.
`Complex(Complex z)` Constructs a separate new `Complex` from an existing `Complex`.
`Complex(double re)` Constructs a `Complex` representing a real number.
`Complex(double re, double im)` Constructs a `Complex` from real and imaginary parts.

Method Summary
`double`	`abs()` Returns the magnitude of a `Complex` number.
`Complex`	`acos()` Returns the principal arc cosine of a `Complex` number.
`Complex`	`acosh()` Returns the principal inverse hyperbolic cosine of a `Complex` number.
`Complex`	`add(Complex z)` To perform z1 + z2, you write `z1.add(z2)` .
`double`	`arg()` Returns the principal angle of a `Complex` number, in radians, measured counter-clockwise from the real axis.
`Complex`	`asin()` Returns the principal arc sine of a `Complex` number.
`Complex`	`asinh()` Returns the principal inverse hyperbolic sine of a `Complex` number.
`Complex`	`atan()` Returns the principal arc tangent of a `Complex` number.
`Complex`	`atanh()` Returns the principal inverse hyperbolic tangent of a `Complex` number.
`static Complex`	`cart(double re, double im)` Returns a `Complex` from real and imaginary parts.
`java.lang.Object`	`clone()` Overrides the `Cloneable` interface.
`Complex`	`conj()` Returns the `Complex` "conjugate".
`Complex`	`cos()` Returns the cosine of a `Complex` number.
`Complex`	`cosec()` Returns the cosecant of a `Complex` number.
`Complex`	`cosh()` Returns the hyperbolic cosine of a `Complex` number.
`Complex`	`cot()` Returns the cotangent of a `Complex` number.
`Complex`	`div(Complex z)` To perform z1 / z2, you write `z1.div(z2)` .
`boolean`	`equals(Complex z, double tolerance)` Decides if two `Complex` numbers are "sufficiently" alike to be considered equal.
`Complex`	`exp()` Returns the number e "raised to" a `Complex` power.
`double`	`im()` Extracts the imaginary part of a `Complex` as a `double`.
`boolean`	`isInfinite()` Returns `true` if either the real or imaginary component of this `Complex` is an infinite value.
`boolean`	`isNaN()` Returns `true` if either the real or imaginary component of this `Complex` is a Not-a-Number (`NaN`) value.
`Complex`	`log()` Returns the principal natural logarithm of a `Complex` number.
`static void`	`main(java.lang.String[] args)` Useful for checking up on the exact version.
`Complex`	`mul(Complex z)` To perform z1 * z2, you write `z1.mul(z2)` .
`Complex`	`neg()` Returns the "negative" of a `Complex` number.
`double`	`norm()` Returns the square of the "length" of a `Complex` number.
`static Complex`	`polar(double r, double theta)` Returns a `Complex` from a size and direction.
`Complex`	`pow(Complex exponent)` Returns this `Complex` raised to the power of a `Complex` exponent.
`static Complex`	`pow(Complex base, Complex exponent)` Returns the `Complex` base raised to the power of the `Complex` exponent.
`static Complex`	`pow(Complex base, double exponent)` Returns the `Complex` base raised to the power of the exponent.
`static Complex`	`pow(double base, Complex exponent)` Returns the base raised to the power of the `Complex` exponent.
`double`	`re()` Extracts the real part of a `Complex` as a `double`.
`static Complex`	`real(double real)` Returns a `Complex` representing a real number.
`Complex`	`scale(double scalar)` Returns the `Complex` scaled by a real number.
`Complex`	`sec()` Returns the secant of a `Complex` number.
`Complex`	`sin()` Returns the sine of a `Complex` number.
`Complex`	`sinh()` Returns the hyperbolic sine of a `Complex` number.
`Complex`	`sqrt()` Returns a `Complex` representing one of the two square roots.
`Complex`	`sub(Complex z)` To perform z1 - z2, you write `z1.sub(z2)` .
`Complex`	`tan()` Returns the tangent of a `Complex` number.
`Complex`	`tanh()` Returns the hyperbolic tangent of a `Complex` number.
`java.lang.String`	`toString()` Converts a `Complex` into a `String` of the form `(`a `+` b`i)`.

ORG.netlib.math.complex Class Complex

AUTHOR

DATE

i

REMARK

TWO_PI

VERSION

Complex

Complex

Complex

Complex

abs

acos

acosh

add

arg

asin

asinh

atan

atanh

cart

clone

conj

cos

cosec

cosh

cot

div

equals

exp

im

isInfinite

isNaN

log

main

mul

neg

norm

polar

pow

pow

pow

pow

re

real

scale

sec

sin

sinh

sqrt

sub

tan

tanh

toString

ORG.netlib.math.complex
Class Complex