// complex3.cpp
// a class that models a complex number data type
// a class that models a complex number data type

#include <iostream.h>
#include <conio.h>               //for getche()
#include <math.h>               //for getche()

class complex_number
{
  private:
    float real;       // real part
    float imaginary;  // imaginery part
    float abs;        // absolute value
    float arg;        // argument
  public:
    void set()
    {
      char dummy;        // for comma
      float a, b;

      cout << "Press i for Re + Im*j or press e for Abs*e^Arg: ";
      dummy = getche();
      if (dummy == 'i')
      {
        cout << "\nEnter Re: ";
        cin >> real;

        cout << "Enter Im: ";
        cin >> imaginary;

        abs = sqrt(real*real + imaginary*imaginary);
        if (real != 0)
          if (real > 0)
            arg = atan(imaginary/real);
          else
            arg = atan(imaginary/real) + M_PI;
        else
          if (real > 0)
            arg = M_PI/2;
          else
            arg = -M_PI/2;
      }
      else
      {
        cout << "\nEnter Abs: ";
        cin >> abs;

        cout << "Enter Arg: ";
        cin >> arg;

        real = abs*cos(arg);
        imaginary = abs*sin(arg);
      }
    }  // void set()

    void display()
    {
      cout << '('
           << real        // real part
           << " , "
           << imaginary   // imaginary part
           << ')';
      cout << " ["
           << abs         // absolute value
           << " * e( i*"
           << arg         // argument
           << " ) ]";
    }

    void add(complex_number compl_num)
    {
      real += compl_num.real;
      imaginary += compl_num.imaginary;
    }

    void mult(complex_number compl_num)
    {
      complex_number cn;
      cn.real = real;
      cn.imaginary = imaginary;

      real = cn.real*compl_num.real - compl_num.imaginary*cn.imaginary;
      imaginary = cn.real*compl_num.imaginary + compl_num.real*cn.imaginary;
    }

    complex_number root_compl_num(int m, int n)
    {
      float phase = arg / n;
      complex_number root;

      root.abs = exp(log(abs)/n);
      root.arg = phase + m*2*M_PI/n;
      root.real = root.abs*cos(root.arg);
      root.imaginary = root.abs*sin(root.arg);

      return root;
    }
};  // class complex_number


void main()
{
  complex_number c1;       // create a complex_number variable
  complex_number c_roots[20];  // create an array of 20 complex_number variable
  int n;

  // enter c1
  cout << "For c1, ";
  c1.set();       // set c1

  // display c1
  cout << "\nc1 = ";
  c1.display();

  // enter the type of the root
  cout << "\nEnter root (n <= 20):";
  cin >> n;

  cout << "\n=== The " << n << "th roots are ===\n";

  // find n roots of c1
  for (int i = 0; i < n; i++)
  {
    c_roots[i] = c1.root_compl_num(i, n);
  }

  // display n roots of c1
  for (int i = 0; i < n; i++)
  {
    // show the i-th root
    cout << "\nroot[" << i + 1 << "] = ";
    c_roots[i].display();           // display c_root[i]
  }

  // stop the flow on the monitor
  getch();

}  //end main