#include <iostream>
#include <string>
#include <cmath>
using namespace std;

class Complex
{
public:
    double real, imag;

    Complex () {
        real = 0.0;  imag = 0.0;
    }

    Complex (double r, double i) {
        real = r;  imag = i;
    }

    double abs () {
        return sqrt (real*real + imag*imag);
    }

    void normalize () {
        double d = abs();
        real = real/d;
        imag = imag/d;
    }

    Complex operator + (const Complex b);

    const Complex& operator = (const Complex b);

};

Complex Complex::operator + (const Complex b) {
    Complex sum (real + b.real, imag + b.imag);
    return sum;
}

const Complex& Complex::operator = (const Complex b) {
    real = b.real;
    imag = b.imag;
    return *this;
}

ostream& operator << (ostream& os, Complex num) {
    os << num.real;
    if (num.imag > 0) {
        os << " + " << num.imag << "i";
    } else if (num.imag < 0) {
        os << " - " << -num.imag << "i";
    }
    return os;
}

int main () {
    Complex y (3.0, 4.0);
    double result = y.abs ();
    cout << "|" << y << "| = " << result << endl;
    Complex num1 (3.0, 2.0), num2 (1.0, 5.0);
    cout << "Your two numbers are " << num1 << " and " << num2 << endl;
    Complex num3 (1, -4);
    cout << num3 << endl;
    Complex realNum (20,0);
    cout << "realNum = " << realNum << endl;
    Complex a, b, c;
    c.real = 1.0;
    c.imag = 2.0;
    a = b = c;
    cout << "a = " << a << ", b = " << b << ", c = " << c << endl;
    a.normalize();
    cout << "a = " << a << endl;
    cout << "|a| = " << a.abs() << endl;
    Complex z (1, 2);
    cout << y + z << endl;

    return 0;
}