Complex Math

This library implements complex number math for JavaScript.

Overview

Complex numbers are pairs of real numbers. (More information about complex numbers.) This library introduces the "Complex" object, which you create and use to hold a number. The constant i is also defined for you (along with I for compatibility with C code). To calculate math, you must use member functions, since JavaScript does not support operator overloading.

For example:

var z = new Complex(3, 2); // Creates the number 3 + 2*i
var w = Exp(i.mul(Math.PI/3)); // Creates the number e^(i*pi/3)

var g = z.mul(w).div(i).sub(1); // Calculates z*w / i - 1

alert(g.toString());

// Result: 2.598076211353316 + i*0.23205080756887675

Complex Member Functions

z.clone();

Returns a full copy of the Complex object.

z.neg();

Returns -z

z.inverse();

Returns 1 / z

z.inverse();

Returns 1 / z

z.add(w);

Returns z + w

z.sub(w);

Returns z - w

z.mul(w);

Returns z * w

z.div(w);

Returns z / w

z.pow(w);

Returns z ^ w

z.abs();

Returns |z|

z.toString();

Returns a string represention of the complex number z.

Functions


//                    _
// Complex Conjugate: z = x - iy
function Conj(z);

// Absolute Value: Abs(z) = sqrt(z.x*z.x + z.y*z.y)
function Abs(z);

// Argument: Arg(z) = theta, the polar angle wrapped to the range (-pi, pi]
function Arg(z);

// Real Part: Re(z) = x
function Re(z);

// Imaginary Part: Im(z) = y
function Im(z);

// Exponential: Exp(z) = e^z
function Exp(z);

// Power: Pow(z, w) = z^w
function Pow(a, b);

// Logarithm: Log(z, w) = ln(Abs(z)) + i*Arg(z)
function Log(z);

// Sine: Sin(z) = (e^(i*z) - e^(-i*z)) / (2*i)
function Sin(z);

// Cosine: Cos(z) = (e^(i*z) + e^(-i*z)) / 2
function Cos(z);

// Gamma Function (A complex extension of the factorial.)
function Gamma(z);