maths
Class Complex

java.lang.Object
  maths.Complex

public class Complex
extends Object

Complex implements a complex number and defines complex arithmetic and mathematical functions Last Updated February 27, 2001 Copyright 1997-2001

Version:

1.0

Author:

Andrew G. Bennett

Constructor Summary

Complex(double u, double v)
Constructs the complex number z = u + i*v

Method Summary

double	arg() Argument of this Complex number (the angle in radians with the x-axis in polar coordinates).
Complex	chs() Negative of this complex number (chs stands for change sign).
Complex	conj() Complex conjugate of this Complex number (the conjugate of x+i*y is x-i*y).
Complex	cos() Cosine of this Complex number (doesn't change this Complex number).
Complex	cosh() Hyperbolic cosine of this Complex number (doesn't change this Complex number).
Complex	div(Complex w) Division of Complex numbers (doesn't change this Complex number).
Complex	exp() Complex exponential (doesn't change this Complex number).
double	imag() Imaginary part of this Complex number (the y-coordinate in rectangular coordinates).
Complex	log() Principal branch of the Complex logarithm of this Complex number.
Complex	minus(Complex w) Subtraction of Complex numbers (doesn't change this Complex number).
double	mod() Modulus of this Complex number (the distance from the origin in polar coordinates).
Complex	plus(Complex w) Addition of Complex numbers (doesn't change this Complex number).
double	real() Real part of this Complex number (the x-coordinate in rectangular coordinates).
Complex	sin() Sine of this Complex number (doesn't change this Complex number).
Complex	sinh() Hyperbolic sine of this Complex number (doesn't change this Complex number).
Complex	sqrt() Complex square root (doesn't change this complex number).
Complex	tan() Tangent of this Complex number (doesn't change this Complex number).
Complex	times(Complex w) Complex multiplication (doesn't change this Complex number).
String	toString() String representation of this Complex number.

Methods inherited from class java.lang.Object

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

Constructor Detail

Complex

public Complex(double u,
               double v)

Constructs the complex number z = u + i*v

Parameters:

u - Real part

v - Imaginary part

Method Detail

real

public double real()

Real part of this Complex number (the x-coordinate in rectangular coordinates).

Returns:

Re[z] where z is this Complex number.

imag

public double imag()

Imaginary part of this Complex number (the y-coordinate in rectangular coordinates).

Returns:

Im[z] where z is this Complex number.

mod

public double mod()

Modulus of this Complex number (the distance from the origin in polar coordinates).

Returns:

|z| where z is this Complex number.

arg

public double arg()

Argument of this Complex number (the angle in radians with the x-axis in polar coordinates).

Returns:

arg(z) where z is this Complex number.

conj

public Complex conj()

Complex conjugate of this Complex number (the conjugate of x+i*y is x-i*y).

Returns:

z-bar where z is this Complex number.

plus

public Complex plus(Complex w)

Addition of Complex numbers (doesn't change this Complex number).
(x+i*y) + (s+i*t) = (x+s)+i*(y+t).

Parameters:

w - is the number to add.

Returns:

z+w where z is this Complex number.

minus

public Complex minus(Complex w)

Subtraction of Complex numbers (doesn't change this Complex number).
(x+i*y) - (s+i*t) = (x-s)+i*(y-t).

Parameters:

w - is the number to subtract.

Returns:

z-w where z is this Complex number.

times

public Complex times(Complex w)

Complex multiplication (doesn't change this Complex number).

Parameters:

w - is the number to multiply by.

Returns:

z*w where z is this Complex number.

div

public Complex div(Complex w)

Division of Complex numbers (doesn't change this Complex number).
(x+i*y)/(s+i*t) = ((x*s+y*t) + i*(y*s-y*t)) / (s^2+t^2)

Parameters:

w - is the number to divide by

Returns:

new Complex number z/w where z is this Complex number

exp

public Complex exp()

Complex exponential (doesn't change this Complex number).

Returns:

exp(z) where z is this Complex number.

log

public Complex log()

Principal branch of the Complex logarithm of this Complex number. (doesn't change this Complex number). The principal branch is the branch with -pi < arg <= pi.

Returns:

log(z) where z is this Complex number.

sqrt

public Complex sqrt()

Complex square root (doesn't change this complex number). Computes the principal branch of the square root, which is the value with 0 <= arg < pi.

Returns:

sqrt(z) where z is this Complex number.

sin

public Complex sin()

Sine of this Complex number (doesn't change this Complex number).
sin(z) = (exp(i*z)-exp(-i*z))/(2*i).

Returns:

sin(z) where z is this Complex number.

cos

public Complex cos()

Cosine of this Complex number (doesn't change this Complex number).
cos(z) = (exp(i*z)+exp(-i*z))/ 2.

Returns:

cos(z) where z is this Complex number.

sinh

public Complex sinh()

Hyperbolic sine of this Complex number (doesn't change this Complex number).
sinh(z) = (exp(z)-exp(-z))/2.

Returns:

sinh(z) where z is this Complex number.

cosh

public Complex cosh()

Hyperbolic cosine of this Complex number (doesn't change this Complex number).
cosh(z) = (exp(z) + exp(-z)) / 2.

Returns:

cosh(z) where z is this Complex number.

tan

public Complex tan()

Tangent of this Complex number (doesn't change this Complex number).
tan(z) = sin(z)/cos(z).

Returns:

tan(z) where z is this Complex number.

chs

public Complex chs()

Negative of this complex number (chs stands for change sign). This produces a new Complex number and doesn't change this Complex number.
-(x+i*y) = -x-i*y.

Returns:

-z where z is this Complex number.

toString

public String toString()

String representation of this Complex number.

Overrides:

toString in class Object

Returns:

x+i*y, x-i*y, x, or i*y as appropriate.