public class Complex {

    private final double re;
    private final double im;

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

    public Complex(double real, double imaginary) {
        re = real;
        im = imaginary;
    }

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

    public Complex(Complex z) {
        re = z.re;
        im = z.im;
    }

    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";
    }

    public double re() {
        return re;
    }

    public double im() {
        return im;
    }

    public boolean isReal() {
        return im == 0;
    }

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

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

    public boolean equals(Complex z) {
        return (re == z.re) && (im == z.im);
    }

    public Complex add(Complex z) {
        double real = re + z.re;
        double imaginary = im + z.im;
        return new Complex(real, imaginary);
    }

    public Complex substract(Complex z) {
        double real = re - z.re;
        double imaginary = im - z.im;
        return new Complex(real, imaginary);
    }

    public Complex multiply(double x) {
        return new Complex(x * re, x * im);
    }

    public Complex multiply(Complex z) {
        double real = re * z.re - im * z.im;
        double imaginary = re * z.im + im * z.re;
        return new Complex(real, imaginary);
    }

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

    public Complex reciprocal() {
        double scale = re * re + im * im;
        return new Complex(re / scale, -im / scale);
    }

    public Complex divide(double x) {
        return new Complex(re / x, im / x);
    }

    public Complex divide(Complex z) {
        return multiply(z.reciprocal());
    }

    public Complex exp() {
        return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
    }

    public Complex sin() {
        return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
    }

    public Complex cos() {
        return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
    }

    public Complex tan() {
        return sin().divide(cos());
    }
}