Complex numbers in JavaScript

Complex.js

var Complex = function(real, imag) {
	if (!(this instanceof Complex)) {
		return new Complex (real, imag);
	}

	if (typeof real === "string" && imag == null) {
		return Complex.parse (real);
	}

	this.real = Number(real) || 0;
	this.imag = Number(imag) || 0;
};

Complex.parse = function(string) {
	var real, imag, regex, match, a, b, c;
	
	// TODO: Make this work better-er
	regex = /^([-+]?(?:\d+|\d*\.\d+))?[-+]?(\d+|\d*\.\d+)?[ij]$/i;
	string = String(string).replace (/\s+/g, '');

	match = string.match (regex);
	if (!match) {
		throw new Error("Invalid input to Complex.parse, expecting a + bi format");
	}

	a = match[1];
	b = match[2];
	c = match[3];

	real = a != null ? parseFloat (a) : 0;
	imag = parseFloat ((b || "+") + (c || "1"));

	return new Complex(real, imag);
};

Complex.prototype.copy = function() {
	return new Complex (this.real, this.imag);
};

Complex.prototype.add = function(operand) {
	var real, imag;

	if (operand instanceof Complex) {
		real = operand.real;
		imag = operand.imag;
	} else {
		real = Number(operand);
		imag = 0;
	}
	this.real += real;
	this.imag += imag;

	return this;
};

Complex.prototype.subtract = function(operand) {
	var real, imag;

	if (operand instanceof Complex) {
		real = operand.real;
		imag = operand.imag;
	} else {
		real = Number(operand);
		imag = 0;
	}
	this.real -= real;
	this.imag -= imag;

	return this;
};
Complex.prototype.multiply = function(operand) {
	var real, imag, tmp;

	if (operand instanceof Complex) {
		real = operand.real;
		imag = operand.imag;
	} else {
		real = Number(operand);
		imag = 0;
	}

	tmp = this.real * real - this.imag * imag;
	this.imag = this.real * imag + this.imag * real;
	this.real = tmp;

	return this;
};

Complex.prototype.divide = function(operand) {
	var real, imag, denom, tmp;

	if (operand instanceof Complex) {
		real = operand.real;
		imag = operand.imag;
	} else {
		real = Number(operand);
		imag = 0;
	}

	denom = real * real + imag * imag;
	tmp = (this.real * real + this.imag * imag) / denom;
	this.imag = (this.imag * real - this.real * imag) / denom;
	this.real = tmp;

	return this;
};


var repl = require('repl');
repl.start().context.Complex = Complex;

No polar coordinates.

@tehmoth MathJS can do.