Consider class Complex shown in Figs. 11.1–11.3. The class enables opera- tions on so-called complex numbers. These are numbers of the form realPart + imaginaryPart * i, where i has the value ?-1

a) Modify the class to enable input and output of complex numbers through the overloaded >> and << operators, respectively (you should remove the print function from the class).
b) Overload the multiplication operator to enable multiplication of two complex numbers as in algebra.
c) Overload the == and != operators to allow comparisons of complex numbers.

Fig. 11.1 Complex class definition.

 // Complex class definition.

 #ifndef COMPLEX_H

 #define COMPLEX_H



 class Complex

 {

 public:

 Complex( double = 0.0, double = 0.0 ); // constructor

 Complex operator+( const Complex & ) const; // addition

 Complex operator-( const Complex & ) const; // subtraction

 void print() const; // output

 private:

 double real; // real part

 double imaginary; // imaginary part

 }; // end class Complex



 #endif

Fig. 11.2 | Complex class member-function definitions.

 // Complex class member-function definitions.

 #include 

 #include "Complex.h" // Complex class definition

 using namespace std;



 // Constructor

 Complex::Complex( double realPart, double imaginaryPart )

 : real( realPart ),

 imaginary( imaginaryPart )

 {

 // empty body

 } // end Complex constructor



 // addition operator

 Complex Complex::operator+( const Complex &operand2 ) const

 {

 return Complex( real + operand2.real,

 imaginary + operand2.imaginary );

 } // end function operator+



 // subtraction operator

 Complex Complex::operator-( const Complex &operand2 ) const

 {

 return Complex( real - operand2.real,

 imaginary - operand2.imaginary );



 } // end function operator-



 // display a Complex object in the form: (a, b)

 void Complex::print() const

 {

 cout << '(' << real << ", " << imaginary << ')';

 } // end function print

Fig. 11.3 | Complex numbers.

 // Complex class test program.

 #include 

 #include "Complex.h"

 using namespace std;



 int main()

 {

 Complex x;

 Complex y( 4.3, 8.2 );

 Complex z( 3.3, 1.1 );



 cout << "x: ";

 x.print();

 cout << "\ny: ";

 y.print();

 cout << "\nz: ";

 z.print();



 x = y + z;

 cout << "\n\nx = y + z:" << endl;

 x.print();

 cout << " = ";

 y.print();

 cout << " + ";

 z.print();



 x = y - z;

 cout << "\n\nx = y - z:" << endl;

 x.print();

 cout << " = ";

 y.print();

 cout << " - ";

 z.print();

 cout << endl;

 } // end main

x: (0, 0)
y: (4.3, 8.2)
z: (3.3, 1.1)
x = y + z:
(7.6, 9.3) = (4.3, 8.2) + (3.3, 1.1)
x = y - z:
(1, 7.1) = (4.3, 8.2) - (3.3, 1.1)

 // Complex class definition.

 #ifndef COMPLEX_H

 #define COMPLEX_H



 #include 

 using namespace std;



 class Complex

 {

 friend ostream &operator<<( ostream &, const Complex & );

 friend istream &operator>>( istream &, Complex & );

 public:

 Complex( double = 0.0, double = 0.0 ); // constructor

 Complex operator+( const Complex& ) const; // addition

 Complex operator-( const Complex& ) const; // subtraction

 Complex operator*( const Complex& ) const; // multiplication

 Complex& operator=( const Complex& ); // assignment

 bool operator==( const Complex& ) const;

 bool operator!=( const Complex& ) const;

 private:

 double real; // real part

 double imaginary; // imaginary part

 }; // end class Complex



 #endif

 // Complex class member-function definitions.

 #include 

 #include "Complex.h"

 using namespace std;



 // Constructor

 Complex::Complex( double realPart, double imaginaryPart )

 : real( realPart ),

 imaginary( imaginaryPart )

 {

 // empty body

 } // end Complex constructor



 // addition operator

 Complex Complex::operator+( const Complex &operand2 ) const

 {

 return Complex( real + operand2.real,

 imaginary + operand2.imaginary );

 } // end function operator+



 // subtraction operator

 Complex Complex::operator-( const Complex &operand2 ) const

 {

 return Complex( real - operand2.real,

 imaginary - operand2.imaginary );



 } // end function operator-





 // Overloaded multiplication operator

 Complex Complex::operator*( const Complex &operand2 ) const

 {

 return Complex(

 ( real * operand2.real ) + ( imaginary * operand2.imaginary ),

 ( real * operand2.imaginary ) + ( imaginary * operand2.real ) );

 } // end function operator*



 // Overloaded = operator

 Complex& Complex::operator=( const Complex &right )

 {

 real = right.real;

 imaginary = right.imaginary;

 return *this; // enables concatenation

 } // end function operator=



 bool Complex::operator==( const Complex &right ) const

 {

 return ( right.real == real ) && ( right.imaginary == imaginary );

 } // end function operator==



 bool Complex::operator!=( const Complex &right ) const

 {

 return !( *this == right );

 } // end function operator!=



 ostream& operator<<( ostream &output, const Complex &complex )

 {

 output << "(" << complex.real << ", " << complex.imaginary << ")";

 return output;

 } // end function operator<<



 istream& operator>>( istream &input, Complex &complex )

 {

 input.ignore(); // skip (

 input >> complex.real;

 input.ignore( 2 ); // skip ',' and space

 input >> complex.imaginary;

 input.ignore(); // skip )

 return input;

 } // end function operator>>

 // Complex class test program.

 #include 

 #include "Complex.h"

 using namespace std;



 int main()

 {

 Complex x, y( 4.3, 8.2 ), z( 3.3, 1.1 ), k;



 cout << "Enter a complex number in the form: (a, b)\n? ";

 cin >> k; // demonstrating overloaded >>

 cout << "x: " << x << "\ny: " << y << "\nz: " << z << "\nk: "

 << k << '\n'; // demonstrating overloaded <<

 x = y + z; // demonstrating overloaded + and =

 cout << "\nx = y + z:\n" << x << " = " << y << " + " << z << '\n';

 x = y - z; // demonstrating overloaded - and =

 cout << "\nx = y - z:\n" << x << " = " << y << " - " << z << '\n';

 x = y * z; // demonstrating overloaded * and =

 cout << "\nx = y * z:\n" << x << " = " << y << " * " << z << "\n\n";



 if ( x != k ) // demonstrating overloaded !=

 cout << x << " != " << k << '\n';



 cout << '\n';

 x = k;



 if ( x == k ) // demonstrating overloaded ==

 cout << x << " == " << k << '\n';

 } // end main

Enter a complex number in the form: (a, b)
? (0, 0)
x: (0, 0)
y: (4.3, 8.2)
z: (3.3, 1.1)
k: (0, 0)
x = y + z:
(7.6, 9.3) = (4.3, 8.2) + (3.3, 1.1)
x = y - z:
(1, 7.1) = (4.3, 8.2) - (3.3, 1.1)
x = y * z:
(23.21, 31.79) = (4.3, 8.2) * (3.3, 1.1)
(23.21, 31.79) != (0, 0)
(0, 0) == (0, 0)