Question

a)Adoubledata field(private)named realfor real part of a complex number.

b)Adoubledata field(private)named imgfor imaginarypart of a complex number.

c)A no-arg constructor that creates a default complex number with real 0and img 0.

d)Auser-defined constructorthat creates a complex number with given 2 numbers.

e)The accessor and mutator functions for realand img.

f)A constant function named addition(Complex&comp1, Complex&comp2) that returns the sum of two givencomplex numbers.

g)Aconstantfunction named subtraction(Complex&comp1, Complex&comp2) that returns the subtractionof two givencomplex numbers.

h)A constant function named multiplication(Complex&comp1, Complex&comp2) that returns the multiplicationof two givencomplex numbers.

i)Write a test program that creates aComplexobject with no-arg constructor.Then, set -4.2 and 3.1to real and imaginary parts of the complex number, respectively.

j)Create another Complexobject using the user-defined constructor.

k)Testaddition, subtractionand multiplication functions using thesetwoComplex objects.

Answer 1

The code for given problem statement:

#include<iostream>
using namespace std;
class Complex
{
    //  access: private
    private:
        double real,img;    //  real and imaginary part of complex number
    //  access: public  
    public:
        Complex()   //  Default constructor
        {
            //  Initializes values to 0
            real=0;
            img=0;
        }
        Complex(double r, double i)
        {
            //  Parameterized constructor
            //  Initializes value at the the time of object creation 
            real=r;
            img=i;
        }
        double R_accessor()     //  For accessing real part  
        {
            return real;
        }
        double I_accessor()     //  For accessing imaginary part 
        {
            return img;
        }
        void R_mutator(double r)    //  For updating value of real part
        {
            real=r;
        }
        void I_mutator(double i)    //  For updating value of imaginary part
        {
            img=i;
        }
        Complex addition(Complex &comp1,Complex &comp2) const
        {
            Complex add;    //  Object of Complex to store addition 
            double r=comp1.R_accessor()+comp2.R_accessor();     //  Addition of real parts
            double i=comp1.I_accessor()+comp2.I_accessor();     //  Addition of imaginary parts
            add.R_mutator(r);
            add.I_mutator(i);
            return add;
        }
        Complex subtraction(Complex &comp1,Complex &comp2) const
        {
            Complex sub;    //  Object of Complex to store subtraction
            double r=comp1.R_accessor()-comp2.R_accessor();     //  Subtraction of real parts
            double i=comp1.I_accessor()-comp2.I_accessor();     //  Subtraction of imaginary parts
            sub.R_mutator(r);
            sub.I_mutator(i);
            return sub;
        }
        Complex multiplication(Complex &comp1,Complex &comp2) const
        {
            Complex mul;    //  Object of Complex to store multiplication
            double r=comp1.R_accessor()*comp2.R_accessor()-comp1.I_accessor()*comp2.I_accessor();   //  To calculate real part
            double i=comp1.R_accessor()*comp2.I_accessor()+comp2.R_accessor()*comp1.I_accessor();   //  To calculate imaginary part
            mul.R_mutator(r);
            mul.I_mutator(i);
            return mul;
        }
};
int main()
{
    Complex a;  //  First object of Complex to initialize to 0+0i
    //  Assigning values to real and imaginary part of 'a'
    a.R_mutator(-4.2);  
    a.I_mutator(3.1);
    Complex b(1.2,2.2);     //  Using user defined parameterized constructor to create and initialize 2nd complex number 
    cout<<"1st complex number is: ";
    cout<<a.R_accessor()<<" + ("<<a.I_accessor()<<"i)"<<"\n";
    cout<<"2nd complex number is: ";
    cout<<b.R_accessor()<<" + ("<<b.I_accessor()<<"i)"<<"\n";
    Complex add=add.addition(a,b);  //  Adding 2 complex numbers and storing into 'add' 
    cout<<"Addition of given complex number is: ";
    cout<<add.R_accessor()<<" + ("<<add.I_accessor()<<"i)"<<"\n";
    Complex sub=sub.subtraction(a,b);  //  subtracting 2 complex numbers and storing into 'subtract' 
    cout<<"Subtraction of given complex number is: ";
    cout<<sub.R_accessor()<<" + ("<<sub.I_accessor()<<"i)"<<"\n";
    Complex mul=mul.multiplication(a,b);  //  multiplying 2 complex numbers and storing into 'add' 
    cout<<"Multiplication of given complex number is: ";
    cout<<mul.R_accessor()<<" + ("<<mul.I_accessor()<<"i)"<<"\n";
    return 0;
}

Screenshot of the code:

Screenshot of output:

Logic of the code:

A class is defned to store a complex number.

Comlex number is written in the form a+bi where a is real part and b is imaginary part and i=sqrt(-1)

There are 2 private data members: One for storing real part and other for storing imaginary part.

There are 2 constructors. One is default constructor to initialize both data members to 0. Second is parameterized constructor to initialize data members to given values when creating the object.

There are 2 mutators. 1 for real part and 2nd for imaginary part. Mutators are functions used to update the data members.

There are 2 accessors. 1 for real part and 2nd for imaginary part. Accessors are functions used to access the data members.

There are 3 constant functions.

1) Addition: Adds real parts and imaginary parts indivisually for provided 2 comlex objects

2) Subtraction: Subtracts real parts and imaginary parts indivisually for provided 2 comlex objects

3) Multiplication: Multiplication of 2 complex numbers is done

The example taken to test code is: -4.2+3.1i and 1.2+2.2i

Addition=(-4.2+1.2)+(3.1+2.2)i= -3 +5.3i

Subtraction=(-4.2-1.2)+(3.1-2.2)i= -5.4+0.9i

multiplication=((-4.2*1.2)-(3.1*2.2))+((-4.2*2.2)+(3.1*1.2))i = -11.86-5.52i