// cplex class with all necessary member functions

#include <math.h>

class cplex
{
	private:
		double	re;
		double	im;
	public:
		cplex (void):
        	re (0.0), im (0.0)  {  }
		cplex (double a, double b):
			re (a), im (b)  {  }
		~cplex (void)  {  }
		cplex (const cplex &rhs):
			re (rhs.re), im (rhs.im) { }
		const cplex & operator= (const cplex &);
		cplex operator+ (const cplex &) const;
		int operator< (const cplex &) const;
		friend istream & operator>> (istream &, cplex &);
		friend ostream & operator<< (ostream &, cplex &);
};


const cplex & cplex::operator= (const cplex &rhs)   // Assignment
{
	if (this != &rhs)
	{ 	re = rhs.re;
		im = rhs.im;
	}
    return *this;
}

cplex cplex::operator+ (const cplex & rhs) const    // Addition
{
	cplex temp;

	temp.re = re + rhs.re;
	temp.im = im + rhs.im;
    return temp;
}

istream & operator>> (istream &in, cplex &rhs)          // Input
{
	in >> rhs.re >> rhs.im;
	return in;
}

ostream & operator<< (ostream &out, cplex &rhs)         // Output
{
	out << "(" << rhs.re << ", " << rhs.im << ")";
    	return out;
}

int cplex::operator< (const cplex &rhs) const     // Compare <
{
	double		d1, d2;

	d1 = sqrt (re*re + im*im);                   // Determine distances
	d2 = sqrt (rhs.re*rhs.re + rhs.im*rhs.im);   // from (0, 0)
	return (d1 < d2) ? 1 : 0;
}