#include "complex2.h"

int operator==(Complex& c1, Complex& c2)
{
   return c1.re()==c2.re() && c1.im()==c2.im();
}

Complex operator+(Complex& c1, Complex& c2)
{
  return Complex(c1.re()+c2.re(), c1.im()+c2.im());
}

Complex operator-(Complex& c1, Complex& c2)
{
  return Complex(c1.re()-c2.re(), c1.im()-c2.im());
}

Complex operator*(Complex& c1, Complex& c2)
{
  // (a+bi).(c+di) = (ac-bd)+(bc+ad)i
  return Complex(c1.re()*c2.re()-c1.im()*c2.im(),
                 c1.im()*c2.re()+c1.re()*c2.im());
}

Complex operator/(Complex& c1, Complex& c2)
{
  Complex num = c1*Complex(c2.re(),-c2.im()); // num = (a+bi).(c-di)
  float   den = c2.re()*c2.re() + c2.im()*c2.im();  // den = (c+di).(c-di) = c^2+d^2
  return Complex(num.re()/den, num.im()/den);
}