Question

You have to implement the other 3 operators, '-', '*', and '/', which are defined as follows. Suppose

Z1 = x1 + y1i
Z2 = x2 + y2i

are complex numbers, then

Z1 - Z2 = (x1 - x2) + (y1 - y2)i

Z₁ * Z₂ = (x₁ x₂ - y₁ y₂) + (x₁ y₂ + x₂ y₁)i

Z₁ / Z₂ = (x₁ x₂ + y₁ y₂) / D + (x₂ y₁ - x₁ y₂)/D i
where

• D = x₂² + y₂²

Answer 1

Here is the code for your problem.

#include <iostream>

#include <cmath>

using namespace std;

class Complex

{

private:

    double real, imag;

public:

    Complex(double r = 0, double i = 0)

    {

        real = r;

        imag = i;

    }

    // This is automatically called when '+' is used with

    // between two Complex objects

    Complex operator+(Complex const &obj)

    {

        Complex res;

        res.real = real + obj.real;

        res.imag = imag + obj.imag;

        return res;

    }

    // This is automatically called when '-' is used with

    // between two Complex objects

    Complex operator-(Complex const &obj)

    {

        Complex res;

        res.real = real - obj.real;

        res.imag = imag - obj.imag;

        return res;

    }

    // This is automatically called when '*' is used with

    // between two Complex objects

    Complex operator*(Complex const &obj)

    {

        Complex res;

        res.real = real * obj.real - imag * obj.imag;

        res.imag = real * obj.imag + obj.real * imag;

        return res;

    }

    // This is automatically called when '/' is used with

    // between two Complex objects

    Complex operator/(Complex const &obj)

    {

        Complex res;

        double D = pow(obj.real, 2) + pow(obj.imag, 2);

        res.real = (real * obj.real + imag * obj.imag) / D;

        res.imag = (obj.real * imag - real * obj.imag) / D;

        return res;

    }

    void print()

    {

        cout << real << " + i" << imag << endl;

    }

};

int main()

{

    Complex c1(10, 5), c2(2, 4);

    Complex c3 = c1 + c2; // An example call to "operator+"

    c3.print();

    c3 = c1 - c2;   // An example call to "operator-"

    c3.print();

    c3 = c1 * c2;   // An example call to "operator*"

    c3.print();

    c3 = c1 / c2;   // An example call to "operator/"

    c3.print();

}

Here is the screenshot of the code if the indentation is not clear.

Here is the output of the code.

Hope this helps.

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