Question

2. A complex number can be expressed as a + bi where a and b are real numbers and i is the imaginary unit. The multiplication of two complex numbers is defined as follows:

(a+bi)(c+di) = (ac-bd) + (bc+ad)i

Define a class which represents a complex number. The only member functions you have to define and implement are those which overload the * and *= symbols.

Answer 1

Given below is the code for question. I have written a main() to show that the implementation is correct
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#include <iostream>
using namespace std;
class Complex{
   private:
   double a, b;
   public:

//constructor with default values for real and imaginary parts
   Complex(double a1 =0 , double b1 = 0){
       a = a1;
       b = b1;
   }

//operator * defined for Complex number

   Complex operator *( const Complex &c){

//use the formula to calculate the real and imaginary parts separately
       double re = a * c.a - b *c.b;
       double im = b * c.a + a * c.b;
       return Complex(re, im); //now create the resulting complex number using the real and imag parts
   }

//performs multiplication of this complex number with the parameter passed and updates this number and returns it  

Complex & operator *= (const Complex &c){
       *this = (*this) * c; //use the already defined * operator to perform multiplication and then update this using =
       return *this; //return a reference to this object
   }

   void print(){
       cout << a << " + " << b << " i" << endl;
   }
};

int main(){
   Complex c1(1, 2), c2(3, 4);
   Complex c3 = c1 * c2;

   cout << "c1 is ";
   c1.print();

   cout << "c2 is ";
   c2.print();

   cout << "c3 is ";
   c3.print();

   cout << "now c3 *= c2" << endl;

   c3 *= c2;

   cout << "c2 is ";
   c2.print();

   cout << "c3 is ";
   c3.print();
}

output
-----

c1 is 1 + 2 i
c2 is 3 + 4 i
c3 is -5 + 10 i
now c3 *= c2
c2 is 3 + 4 i
c3 is -55 + 10 i

Answer 2