Complex.js

/**
 * Instances of this Complex class 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.
 */
class Complex {
    // Once class field declarations are standardized, we could declare
    // private fields to hold the real and imaginary parts of a complex number
    // here, with code like this:
    //
    // #r = 0;
    // #i = 0;

    // This constructor function defines the instance fields r and i on every
    // instance it creates. These fields hold the real and imaginary parts of
    // the complex number: they are the state of the object.
    constructor(real, imaginary) {
        this.r = real;       // This field holds the real part of the number.
        this.i = imaginary;  // This field holds the imaginary part.
    }

    // Here are two instance methods for addition and multiplication
    // of complex numbers. If c and d are instances of this class, we
    // might write c.plus(d) or d.times(c)
    plus(that) {
        return new Complex(this.r + that.r, this.i + that.i);
    }
    times(that) {
        return new Complex(this.r * that.r - this.i * that.i,
                           this.r * that.i + this.i * that.r);
    }

    // And here are static variants of the complex arithmetic methods.
    // We could write Complex.sum(c,d) and Complex.product(c,d)
    static sum(c, d) { return c.plus(d); }
    static product(c, d) { return c.times(d); }

    // These are some instance methods that are defined as getters
    // so they're used like fields. The real and imaginary getters would
    // be useful if we were using private fields this.#r and this.#i
    get real() { return this.r; }
    get imaginary() { return this.i; }
    get magnitude() { return Math.hypot(this.r, this.i); }

    // Classes should almost always have a toString() method
    toString() { return `{${this.r},${this.i}}`; }

    // It is often useful to define a method for testing whether
    // two instances of your class represent the same value
    equals(that) {
        return that instanceof Complex &&
            this.r === that.r &&
            this.i === that.i;
    }

    // Once static fields are supported inside class bodies, we could
    // define a useful Complex.ZERO constant like this:
    // static ZERO = new Complex(0,0);
}

// Here are some class fields that hold useful predefined complex numbers.
Complex.ZERO = new Complex(0,0);
Complex.ONE = new Complex(1,0);
Complex.I = new Complex(0,1);