A complex number is of the form x+iy, where i²=-1. x, y are called real and imaginary part of the complex number. Complex numbers have vast applications in mathematics, physics, and engineering. They have an arithematic governed by a series of rules including the following:
 

    Let u = a + ib,  v = c + id
    |u|=sqrt(a² + b²)  // Magnitude
    u + v = (a + c) + i(b + d)
    u - v = (a - c) + i(b - d)
    u * v = (ac - bd) + i(ad + bc)
    u / v = (ac + bd)/(c² + d²) + i(bc - ad)/(c² + d²)

In three different ways implement the class complex whose declaration is

//version 1.
class complex {
private:
   double  real, imag;
public:
   complex(double r, double i) {real = r; imag = i;}
   complex() {real = 0.0, imag = 0.0;}
   void print()const; //print complex form: x + iy
   double magnitude()const;
   complex add_c(const complex& a, const complex& b);
   complex mult_c(const complex& a, const complex& b);
   complex div_c(const complex& a, const complex& b);
};

//version 2.
class complex {
private:
   double  real, imag;
public:
   complex(double r, double i) {real = r; imag = i;}
   complex() {real = 0.0, imag = 0.0;} //default constructor
   void print()const; //print complex form: x + iy
   double magnitude()const;
   friend complex operator+ (const complex& a, const complex& b);
   friend complex operator- (const complex& a, const complex& b);
   friend complex operator* (const complex& a, const complex& b);
   friend complex operator/ (const complex& a, const complex& b);
};

//version 3.
class complex {
private:
   double  real, imag;
public:
   complex(double r, double i) {real = r; imag = i;}
   complex() {real = 0.0, imag = 0.0;} //default constructor
   friend ostream& operator<< (ostream& ostr, const complex& c);
   double magnitude()const
   complex operator+ (const complex& a) const;
   complex operator- (const complex& a) const;
   complex operator* (const complex& a) const;
   complex operator/ (const complex& a) const;
};

In each version write a simple calculator to test addition, substraction multiplication and division of two complex numbers. Also print out the magnitude of the result of these operations.