/* * Complex.js: * This file defines a Complex class to represent complex numbers. * Recall that a complex number is the sum of a real number and an * imaginary number, and that the imaginary number i is the * square-root of -1. */ * The first step in defining a class is defining the constructor * function of the class. This constructor should initialize any * instance properties of the object. These are the essential * "state variables" that make each instance of the class different. */ function Complex(real, imaginary) { this.x = real; // The real part of the number this.y = imaginary; // The imaginary part of the number } /* * The second step in defining a class is defining its instance * methods (and possibly other properties) in the prototype object * of the constructor. Any properties defined in this object will * be inherited by all instances of the class. Note that instance * methods operate implicitly on the "this" keyword. For many methods * no other arguments are needed. */ // Return the magnitude of a complex number. This is defined // as its distance from the origin (0,0) of the complex plane. Complex.prototype.magnitude = function() { return Math.sqrt(this.x*this.x + this.y*this.y); }; // Return a complex number that is the negative of this one. Complex.prototype.negative = function() { return new Complex(-this.x, -this.y); }; // Convert a Complex object to a string in a useful way. // This is invoked when a Complex object is used as a string. Complex.prototype.toString = function() { return "{" + this.x + "," + this.y + "}"; }; // Return the real portion of a complex number. This function // is invoked when a Complex object is treated as a primitive value. Complex.prototype.valueOf = function() { return this.x; } /* * The third step in defining a class is to define class methods, * constants, and any needed class variables as properties of the * constructor function itself (instead of as properties of the * prototype object of the constructor). Note that static methods * do not use the "this" keyword: they operate only on their arguments. */ // Add two complex numbers and return the result. Complex.add = function (a, b) { return new Complex(a.x + b.x, a.y + b.y); }; // Subtract one complex number from another. Complex.subtract = function (a, b) { return new Complex(a.x - b.x, a.y - b.y); }; // Multiply two complex numbers and return the product. Complex.multiply = function(a, b) { return new Complex(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x); }; // Here are some useful predefined complex numbers. // They are defined as Class variables, where they can be used as // "constants." (Note, though that they are not actually read-only.) Complex.zero = new Complex(0,0); Complex.one = new Complex(1,0); Complex.i = new Complex(0,1);