algebra.js/src/complex.js

Build, display, and solve algebraic equations.

var Expression = require('./expressions').Expression;
var isInt = require('./helper').isInt;
var Fraction = require('./fractions');

var Complex = function(real, imaginary) {
    if (real instanceof Fraction && imaginary instanceof Fraction) {
        this.real = real;
        this.imaginary = imaginary;
    } else {
        throw new TypeError("Invalid Argument (" + real.toString() + ", " + imaginary.toString() + "): Real and imaginary parts must be of type Fraction.");
    }
};

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

Complex.prototype.add = function(a) {
    var copy = this.copy();

    if (a instanceof Fraction || isInt(a)) {
        copy.real = copy.real.add(a);
    } else if (a instanceof Complex) {
        copy.real = copy.real.add(a.real);
        copy.imaginary = copy.imaginary.add(a.imaginary);
    } else {
        throw new TypeError("Invalid Argument (" + a.toString() + "): Summand must be of type Complex, Fraction or Integer.");
    }

    return copy;
};

Complex.prototype.subtract = function(a) {
    var copy = this.copy();

    if (a instanceof Fraction || isInt(a)) {
        copy.real = copy.real.subtract(a);
    } else if (a instanceof Complex) {
        copy.real = copy.real.subtract(a.real);
        copy.imaginary = copy.imaginary.subtract(a.imaginary);
    } else {
        throw new TypeError("Invalid Argument (" + a.toString() + "): Subtrahend must be of type Complex, Fraction or Integer.");
    }

    return copy;
};

Complex.prototype.multiply = function(a) {
    if (a instanceof Fraction || isInt(a)) {
        var copy = this.copy();
        copy.real = copy.real.multiply(a);
        copy.imaginary = copy.imaginary.multiply(a);
        return copy;
    } else if (a instanceof Complex) {
        var expr1 = new Expression("i").multiply(this.imaginary).add(this.real);
        var expr2 = new Expression("i").multiply(a.imaginary).add(a.real);
        var foil = expr1.multiply(expr2);
        var coefs = foil._quadraticCoefficients();
        var a = coefs.a;
        var b = coefs.b;
        var c = coefs.c;

        var real = a.multiply(-1).add(c);
        return new Complex(real, b);
    } else {
        throw new TypeError("Invalid Argument (" + a.toString() + "): Multiplicand must be of type Complex, Fraction or Integer.");
    }
};

Complex.prototype.divide = function(a) {
    if (a instanceof Fraction || isInt(a)) {
        var copy = this.copy();
        copy.real = copy.real.divide(a);
        copy.imaginary = copy.imaginary.divide(a);
        return copy;
    } else if (a instanceof Complex) {
        var conjugate = new Complex(a.real, a.imaginary.multiply(-1));
        var numerator = this.multiply(conjugate);
        var denominator = a.multiply(conjugate).real;
        return numerator.divide(denominator);
    } else {
        throw new TypeError("Invalid Argument (" + a.toString() + "): Divisor must be of type Complex, Fraction or Integer.");
    }
};

module.exports = Complex;