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.

In C++ please, thank you

Answer 1

Given below is the code for question. I have written a main() to show that the implementation is correct
Please do rate the answer if it helped. thank you.

#include <iostream>
using namespace std;
class Complex{
   private:
   double a, b;
   public:
   Complex(double a1 =0 , double b1 = 0){
       a = a1;
       b = b1;
   }

   Complex operator *( const Complex &c){
       double re = a * c.a - b *c.b;
       double im = b * c.a + a * c.b;
       return Complex(re, im);
   }

   Complex & operator *= (const Complex &c){
       *this = (*this) * c;
       return *this;
   }

   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