//thanks for C. Dutoit for the algorithms


#ifndef COMPLEX_H

#define COMPLEX_H


class Complex
{
public:

	// constructors

	Complex();    // 0 + i*0

	Complex(double a, double b); // a + i*b

	Complex(double a); // a + i*0


	// friends

	//friend ostream& operator<<(ostream&, Complex); // print as <re,im>

	friend Complex operator+(Complex,Complex); // addition of two Complex numbers

	friend Complex operator-(Complex,Complex); // subtraction of two Complex numbers

	friend Complex operator*(Complex,Complex); // multiplication of two Complex numbers


	// members 

	Complex operator-(); // return <-re,-im>

	double modulus();    // return sqrt(re*re+im*im)

	double real();       // return re

	double imag();       // return im

    Complex root();      // return the sqrt(re + i*im)



private:
	// real and imaginary parts

	double re;
	double im;
};

const Complex i(0,1);


#endif