#include <iostream.

#include <iostream.h>
#include <stdio.h>
#include <math.h>

#define ZERO 1.0E-20
#define PI 3.141592654
#define true 1
#define false 0

class complex { // 복소수형에 대한 연산자의 다중정의.
private :
double x, y;

   public :
      complex(double r=0, double i=0) { x=r; y=i; }   // 생성자
      void print();
      friend complex operator+(complex, complex);
      friend complex operator-(complex, complex);
      friend complex operator*(complex, complex);
      friend complex operator/(complex, complex);

friend double abs(complex);
friend complex sqrt(complex);
};

void complex::print()
{
printf("%5.2f+%5.2fi", x, y);
}

complex operator+(complex a, complex b) // 더하기 연산의 다중정의
{
return (complex(a.x+b.x, a.y+b.y));
}

complex operator-(complex a, complex b) // 빼기 연산의 다중정의
{
return (complex(a.x-b.x, a.y-b.y));
}

complex operator*(complex a, complex b) // 곱하기 연산의 다중정의
{
return (complex(a.x*b.x-a.y*b.y, a.x*b.y+a.y*b.x));
}

complex operator/(complex a, complex b) // 나누기 연산의 다중정의
{
   return ( complex( (a.x*b.x+a.y*b.y)/(b.x*b.x+b.y*b.y), \
                     (a.y*b.x-a.x*b.y)/(b.x*b.x+b.y*b.y)) );
}

double abs(complex a)
{
return (sqrt((a.x*a.x+a.y*a.y)));
}

complex sqrt(complex a)
{
double r, t;
double hp = 0.5 * PI;

   if (fabs(a.x) <= ZERO) {
      if (fabs(a.y) <= ZERO) {
         r=0.; t=0.;
      } else {
         t = hp;
         if (a.y < 0.) t = -t;
         r = fabs(a.y);
      }
   } else {
      r = sqrt(a.x*a.x+a.y*a.y);
      if(fabs(a.y) < ZERO) {
         t = 0.;
         if(a.x < 0.) t = PI;
      }
   }

return ( complex(sqrt(r)*cos(0.5*t), sqrt(r)*sin(0.5*t)) );
}

void main()
{
    complex a, b;

    a = complex(1,3);
    b=sqrt(a);
    b.print();
}