Question

Problem 2 (C++):

Design and implement a class complexType, that can be used to process complex numbers.

A number of the form a +ib, in which i² = -1 and a and b are real numbers, is called a complex number. We call a the real part and b the imaginary part of a + ib.

Complex numbers can also be represented as ordered pairs (a, b).

The class you will design should have the following features.

Constructor

Your class should have a default constructor as well as a parametrized constructor (which requires 2 double arguments).

Accessor functions required

Your class should implement the following member functions:

setComplex – set the real and imaginary parts of the complex number

getComplex – get the real and imaginary parts complex number

Operator Overloading

The class must overload and implement the following operators:

Stream I/O

• Extend the definition of the class complexType so that it overloads stream insertion and extraction operators

To output a complex number in the form (a, b)

in which a is the real part and b is the imaginary part, the algorithm is as follows:

1. Output the left parenthesis, (.
2. Output the real part.
3. Output the comma and a space.
4. Output the imaginary part.
5. Output the right parenthesis, ).

The algorithm to read this complex number is as follows:

1. Read and discard the left parenthesis.
2. Read and store the real part.
3. Read and discard the comma.
4. Read and store the imaginary part.
5. Read and discard the right parenthesis.

• + and -: Extend the class to perform addition addition and subtraction operations. Overload the operators addition and subtraction for this class as member functions and define the functions.

If (a, b) and (c, d) are complex numbers:

(a, b) + (c, d) = (a + c, b + d)

(a, b) - (c, d) = (a - c, b - d)

• * and /: Extend the class to perform the multiplication and division operations. Overload the operators multiplication and division for this class as member functions and define the functions.

If (a, b) and (c, d) are complex numbers:

((a, b) * (c, d) = ac +ad + bc +bd

If (c, d) is nonzero:

(a, b)/(c, d)=((ac +bd)/(c² +d² ), (-ad +bc)/( c² +d²))

• =: The class must implement = assignment statement as well.

Answer 1

C++ code

#include<iostream>
using namespace std;

class complexType{
   private:
       double real,imag;
      
   public:
       complexType(){
           real = 0;
           imag = 0;
       }
       complexType(double r , double i){
           real = r;
           imag = i;
       }
      
       void setReal(double r){
           real = r;
       }
       void setImag(double i){
           imag = i;
       }
       double getReal(){
           return real;
       }
       double getImag(){
           return imag;
       }
      
       complexType& operator+(const complexType& other){
           double r = real + other.real;
           double i = imag + other.imag;
          
           return *(new complexType(r , i));
       }
      
       complexType& operator-(const complexType& other){
           double r = real - other.real;
           double i = imag - other.imag;
          
           return *(new complexType(r , i));
       }
      
       complexType& operator*(const complexType& other){
           double r = real * other.real - imag*other.imag;
           double i = imag*other.real + real*other.imag;
          
           return *(new complexType(r , i));
       }
      
       complexType& operator/(const complexType& other){
           double val = (other.real* other.real + other.imag*other.imag);
           double r = (real * other.real + imag*other.imag)/val;
           double i = (imag*other.real - real*other.imag)/val;
          
           return *(new complexType(r , i));
       }
      
       friend ostream& operator << (ostream& out , const complexType& other){
           out<<"("<<other.real<<", "<<other.imag<<")";
           return out;
       }
      
       friend istream& operator >> (istream& in , complexType& other){
           char ch;
           in>>ch>>other.real>>ch>>other.imag>>ch;
           return in;
       }
};

int main(){
   complexType c1(2,3);
   complexType c2,c3;
   cin>>c2;
   c3 = c1 + c2;
   cout<<"c1 + c2 = "<<c3<<endl;
  
   c3 = c1 - c2;
   cout<<"c1 - c2 = "<<c3<<endl;
  
   c3 = c1 * c2;
   cout<<"c1 * c2 = "<<c3<<endl;
  
   c3 = c1 / c2;
   cout<<"c1 / c2 = "<<c3<<endl;
  
   return 0;
  
}