// ----------
// complexx.h
// ----------

// Project 2 of Com S 229
// Due at 11:59pm on Monday, Sep 28, 2009
// 
// Implement the following class. 

#ifndef COMPLEX_H
#define COMPLEX_H

#include <cmath>
#include <iostream>
using namespace std; 

class complex
{
  // friend functions are defined outside the public & private sections.
  friend ostream& operator<< (ostream& ostr, const complex& x); // see proj2.pdf 
  friend istream& operator>> (istream& istr, complex& x);       // for input/output formats. 

 public: 
  complex (double x = 0.0, double y = 0.0); // constructor

  // access member functions 
  double realPart() const;   // return real part 
  double imagPart() const;   // return imaginary part 
  double magnitude() const;  // return magnitude
  double phase() const;      // return phase
  
  complex sqrt() const;       // square root with nonnegative real part
  complex pow(int n) const;   // nth power, more efficiently implemented using magnitude and
                              // phase angle.
                            
  complex operator+ (const complex& rhs); // complex addition
  complex operator- (const complex& rhs); // complex subtraction
  complex operator* (const complex& rhs); // complex multiplication
  complex operator/ (const complex& rhs); // complex division 
  bool operator== (const complex& rhs); // equality

  complex operator-() const;   // negation of a complex number 

 private: 
  double real; // real part
  double imag; // imaginary part
}; 


// evaluate the polynomial f(z) = z^3 - 3 z^2 + 4 z - 2
complex f(const complex& z); 


#endif