Class Complex

Object
   |
   +----Complex

public class Complex

extends Object

Version:

1.0

Author:

Andrew G. Bennett

Complex(double, double)

Constructs the complex number z = u + i*v

arg()

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

chs()

Negative of this complex number (chs stands for change sign).

conj()

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

cos()

Cosine of this Complex number (doesn't change this Complex number).

cosh()

Hyperbolic cosine of this Complex number (doesn't change this Complex number).

div(Complex)

Division of Complex numbers (doesn't change this Complex number).

exp()

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

imag()

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

log()

Principal branch of the Complex logarithm of this Complex number.

minus(Complex)

Subtraction of Complex numbers (doesn't change this Complex number).

mod()

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

plus(Complex)

Addition of Complex numbers (doesn't change this Complex number).

real()

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

sin()

Sine of this Complex number (doesn't change this Complex number).

sinh()

Hyperbolic sine of this Complex number (doesn't change this Complex number).

sqrt()

Complex square root (doesn't change this complex number).

tan()

Tangent of this Complex number (doesn't change this Complex number).

times(Complex)

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

toString()

String representation of this Complex number.

public Complex(double u,
               double v)

Constructs the complex number z = u + i*v

Parameters:

u - Real part

v - Imaginary part

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.

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.

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.

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.

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.

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

public Complex exp()

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

Returns:

exp(z) where z is this Complex number.

public double imag()

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

Returns:

Im[z] where z is this Complex number.

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.

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.

public double mod()

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

Returns:

|z| where z is this Complex number.

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.

public double real()

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

Returns:

Re[z] where z is this Complex number.

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.

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.

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.

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.

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.

public java.lang.String toString()

String representation of this Complex number.

Returns:

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

Overrides:

toString in class Object