ComplexNumbers

/*
 * Ricardo Santiago
 * Complex Numbers
 * CSC-112
 * 2/19/2016
 */

public class Complex {

//finalize the variables to make immutable
    private final double re;
    private final double im;

    public Complex(double real, double imag) {
        this.re = real;
        this.im = imag;
    }

    public Complex(double real) {
        this.re = real;
        this.im = 0;
    }

    public Complex() {
        this.re = 0;
        this.im = 0;
    }

    public Complex add(Complex c) {
        Complex a = this;
        double real = a.re + c.re;
        double imag = a.im + c.im;
        return new Complex(real, imag);
    }

    public Complex subtract(Complex c) {
        Complex a = this;
        return a.add(c.negate());
    }

    public Complex multiply(Complex c) {
        Complex a = this;
        double real = (a.re * c.re) - (a.im * c.im);
        double imag = (a.re * c.im) + (a.im * c.re);
        return new Complex(real, imag);
    }

    // I am currently looking for a faster method to calculate this, possibly using conjugate
    public Complex divide(Complex c) {
        Complex a = this;
        double real = ((a.re * c.re) + (a.im * c.im)) / ((c.re * c.re) + (c.im * c.im));
        double imag = ((a.im * c.re) - (a.re * c.im)) / ((c.re * c.re) + (c.im * c.im));
        return new Complex(real, imag);
    }

    public double abs() {
        return Math.hypot(re, im);
    }

    public Complex negate() {
        return new Complex(-re, -im);
    }

    public Complex conjugate() {
        return new Complex(re, -im);
    }

    public double distance(Complex c) {
        return this.subtract(c).abs();

    }

    public boolean equals(Complex c) {
        double diff;
        if (this.greaterThan(c) == true)
            diff = (this.abs() - c.abs()) / this.abs();
        else
            diff = (c.abs() - this.abs()) / c.abs();

        if (diff < 1E-6)
            return true;
        else
            return false;
    }

    public boolean greaterThan(Complex c) {
        if (this.abs() > c.abs())
            return true;
        else
            return false;
    }

    public boolean lessThan(Complex c) {
        if (this.abs() < c.abs())
            return true;
        else
            return false;
    }

    public String toString() {
        if (im == 0)
            return re + "";
        if (re == 0)
            return im + "i";
        if (im < 0)
            return re + " - " + (-im) + "i";
        return re + " + " + im + "i";
    }

}