#include <cmath>
#include "complex.h"

// The values for the default arguments only appear in the class declaration
Complex::Complex(double x, double y) : real_(x), imag_(y) {}

// Copy constructor
Complex::Complex(Complex const& old) : real_(old.real_), imag_(old.imag_) {}

// Assignment operator
Complex& Complex::operator= (Complex const& rhs) {
  real_ = rhs.real_;
  imag_ = rhs.imag_;
  return *this;
}

// Compute and return the magnitude of the complex number.
double Complex::Magnitude() const {
  return sqrt(real_*real_ + imag_*imag_);
}

// Addition operator as a member function.
Complex Complex::operator+ (Complex const& rhs) const {
  double re = real_ + rhs.real_;
  double im = imag_ + rhs.imag_;
  return Complex(re, im);
}

// Subtraction operator as a non-member function.
Complex operator- (Complex const& lhs, Complex const& rhs) {
  return Complex(lhs.Real()-rhs.Real(), lhs.Imaginary()-rhs.Imaginary());
}

// Unary negation operator.  Note that there are no arguments.
Complex Complex::operator- () const {
  return Complex(-real_, -imag_);
}

// Input stream operator as a friend function
istream& operator>> (istream & istr, Complex & c) {
  istr >> c.real_ >> c.imag_;
  return istr;
}

// Output stream operator as an ordinary non-member function
ostream& operator<< (ostream & ostr, Complex const& c) {
  if (c.Imaginary() < 0)  ostr << c.Real() << " - " << -c.Imaginary() << " i ";
  else                    ostr << c.Real() << " + " << c.Imaginary() << " i ";
  return ostr;
}