#include "Complex.h"

#include <iostream>
#include <cmath>

// class implementation
Complex::Complex(double re, double im)  : theReal(re), theImag(im){
}

double Complex::re() const {
  return theReal;
}

double Complex::im() const {
  return theImag;
}

double Complex::mag() const {
  return sqrt(mag2());
}

double Complex::mag2() const {
  return theReal*theReal+theImag*theImag;
}

Complex Complex::coniugate() const {
  return Complex(re(),-im());
}

Complex Complex::inverse() const {
  return 1./mag2()*coniugate();
}

Complex operator+(const Complex&  lhs, const Complex&  rhs){
  return Complex(lhs.re() + rhs.re(), lhs.im() + rhs.im());
}

Complex operator-(const Complex& rhs){
  return Complex(-rhs.re(), -rhs.im());
}

Complex operator-(const Complex& lhs, const Complex& rhs){
  return Complex(lhs.re() - rhs.re(), lhs.im() - rhs.im());
}

Complex operator*(const Complex& lhs, const Complex& rhs){
  return Complex(lhs.re()*rhs.re()-lhs.im()*rhs.im(),
                 lhs.im()*rhs.re()+rhs.im()*lhs.re());
}

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

std::ostream& operator<<(std::ostream& out , const Complex& c) {
  out << "(" << c.re() << (c.im()>=0. ? "+i" : "-i") << fabs(c.im()) << ")";
  return out;
}