// complex number class

class Complex { 
  friend bool operator==(const Complex &a, const Complex &b);
  friend Complex operator+(const Complex &a, const Complex &b);
  friend Complex operator-(const Complex &a, const Complex &b);
 private:
  double real, imaginary;

 public:
  Complex( double r, double i = 0 ) : real(r), imaginary(i) {}
  Complex( Complex &c ) : real(c.real), imaginary(c.imaginary) {}
};

// equality comparison of complex numbers
bool operator==(const Complex &a, const Complex &b)
{ 
  return a.real == b.real  &&  a.imaginary == b.imaginary; 
}

// addition of complex numbers
Complex operator+(const Complex &a, const Complex &b) {
  Complex temp(0,0);
  temp.real = a.real + b.real;
  temp.imaginary = a.imaginary + b.imaginary;
  return temp;
}

// subtraction of complex numbers
Complex operator-(const Complex &a, const Complex &b) {
  Complex temp(0,0);
  temp.real = a.real - b.real;
  temp.imaginary = a.imaginary - b.imaginary;
  return temp;
}