Problem Description: Declare and define a class for a complex number. A complex

Question

Problem Description:

Declare and define a class for a complex number. A complex number in mathematics is defined as x+yi , where x defines the real part of the number and y is the imaginary part.

Requirements (Program to be written in C++):

Define a complex class that has the following member functions:

o constructor that initializes the complex number by default arguments

o set function that sets the real part of the complex number

o set function that sets the imaginary part of the complex number

o get function that returns the real part of the complex number

o get function that returns the imaginary part of the complex number

o a function that displays the complex number

Add the following nonmember functions in your complex header file and implementation file :

o A function that returns the sum of two complex numbers

o A function that returns the difference of two complex numbers

o A function that returns the product of two complex numbers

o A function that returns the quotient of two complex numbe

Write the class in header and implementation files , and compile it separately from the client program

Explanation / Answer

Here is the header file:

#include <iostream>
#ifndef COMPLEX_H
#define COMPLEX_H
class Complex
{
    // A complex number in mathematics is defined as x+yi ,
    //where x defines the real part of the number and y is the imaginary part.
    double real;
    double imag;
    public:
        //o constructor that initializes the complex number by default arguments
        Complex();
        Complex(double, double);
        //o set function that sets the real part of the complex number
        void setReal(double);
        //o set function that sets the imaginary part of the complex number
        void setImag(double);
        //o get function that returns the real part of the complex number
        double getReal();
        //o get function that returns the imaginary part of the complex number
        double getImag();
        //o a function that displays the complex number
        void display();
};

//Add the following nonmember functions in your complex header file and implementation file :
//o A function that returns the sum of two complex numbers
Complex add(Complex, Complex);
//o A function that returns the difference of two complex numbers
Complex diff(Complex, Complex);
//o A function that returns the product of two complex numbers
Complex mul(Complex, Complex);
//o A function that returns the quotient of two complex numbers
Complex div(Complex, Complex);
#endif

And the .cpp file is:

#include <iostream>
#include "Complex.h"
using namespace std;
Complex::Complex()
{
    real = imag = 0;
}
Complex::Complex(double real, double imag)
{
    this->real = real;
    this->imag = imag;
}
void Complex::setReal(double real) { this->real = real; }
void Complex::setImag(double imag) { this->imag = imag; }

double Complex::getReal() { return real; }
double Complex::getImag() { return imag; }

void Complex::display()
{
    cout << real << "+" << imag << "i" << endl;
}

Complex add(Complex first, Complex second)
{
    return Complex(first.getReal() + second.getReal(), first.getImag() + second.getImag());
}

Complex diff(Complex first, Complex second)
{
    return Complex(first.getReal() - second.getReal(), first.getImag() - second.getImag());
}

Complex mul(Complex first, Complex second)
{
    return Complex(first.getReal() * second.getReal() - first.getImag() * second.getImag(), first.getImag() * second.getReal() + second.getImag() * first.getReal());
}
Complex div(Complex first, Complex second)
{
    double denominator = second.getReal() * second.getReal() + second.getImag() * second.getImag();
    double realTemp = (first.getReal() * second.getReal() + first.getImag() * second.getImag()) / denominator;
    double imagTemp = (first.getImag() * second.getReal() - first.getReal() * second.getImag()) / denominator;
    return Complex(realTemp, imagTemp);
}

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