#include <iostream>
#include <cmath>

class Complex
{
public:
  Complex(double = 0., double = 0.);
  double real() ;
  double imag()   {
    return m_imag;
  }
  double mag()  ;
  double mag2()  ;
  Complex coniugate()  ;
  Complex inverse()  ;
  Complex operator+=(Complex  rhs);

 private:
  double m_real;
  double m_imag;
};

inline double Complex::real() {
  return m_real;
}

Complex operator+(Complex  lhs, Complex  rhs);
Complex operator-(Complex  lhs, Complex  rhs);
Complex operator*(Complex  lhs, Complex  rhs);
Complex operator/(Complex  lhs, Complex  rhs);
Complex operator-(Complex  lhs);
double abs(Complex  c);

std::ostream& operator<<(std::ostream&, Complex );

Complex::Complex(double re, double im)  : m_real(re), m_imag(im){
}

Complex Complex::operator+=(Complex  rhs) {
  m_real += rhs.m_real;
  m_imag += rhs.m_imag;
  
  return *this;
}

Complex operator-(Complex  rhs){
  return Complex(-rhs.real(), -rhs.imag());
}

Complex operator+(Complex  lhs, Complex  rhs){
  return Complex(lhs.real() + rhs.real(), lhs.imag() + rhs.imag());
}

Complex operator-(Complex  lhs, Complex  rhs){
  return Complex(lhs.real() - rhs.real(), lhs.imag() - rhs.imag());
}

std::ostream& operator<<(std::ostream& os, Complex  c){
  //(re,im)
  os << '(' << c.real() << ',' << c.imag() << ')';
  return os;
}

//   cout <<c2    --->  operator<<(cout,c2)

Complex operator*(Complex  lhs, Complex  rhs){
  return Complex(lhs.real()*rhs.real()-lhs.imag()*rhs.imag(), lhs.imag()*rhs.real()+ rhs.imag()*lhs.real());
}

Complex operator/(Complex  lhs, Complex  rhs){
  return lhs*rhs.inverse();
}


Complex Complex::coniugate()  {
  return Complex(real(),-imag());
}
Complex Complex::inverse()  {
  return 1./mag2()*coniugate();
}
double Complex::mag2()  {
  return (real()*real()+imag()*imag());
}
double Complex::mag()  {
  return sqrt(real()*real()+imag()*imag());
}