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

// Project 2 of Com S 229
// Due at 11:59pm on Wednesday, Oct 5, 2011
// 
// Implement the following class. 

#include <math.h>
#include <iostream>
using namespace std; 

const double pi = 3.14159265358979323846;
const double epsilon = 0.00001;

class complex
{
 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 

  friend ostream& operator<< (ostream& ostr, const complex& x); // see Section 3.1 of hw2-project.pdf 
  friend istream& operator>> (istream& istr, complex& x);       // for input/output formats. 

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


// evaluate the polynomial f(z) = z^8 - 170 z^6 + 7392 z^4 - 39712 z^2 + 51200
complex f(const complex& z);