Complex.java

public class Complex {
    public double re;
    public double im;

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

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

    public double arg() {
        return Math.atan2(this.im, this.re);
    }

    public Complex add(Complex other) {
        return new Complex(this.re + other.re, this.im + other.im);
    }

    public Complex sub(Complex other) {
        return new Complex(this.re - other.re, this.im - other.im);
    }

    public Complex mul(Complex other) {
        return new Complex(
                this.re * other.re - this.im * other.im,
                this.re * other.im + other.re * this.im);
    }

    public Complex div(Complex other) {
        double denom = other.re * other.re + other.im * other.im;

        return new Complex(
                (this.re * other.re + this.im * other.im) / denom,
                (other.re * this.im - this.re * other.im) / denom);
    }

    @Override
    public String toString() {
        return this.re + (Math.signum(this.im) < 0 ? "-" : "+") + this.im + "i";
    }
}