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Logic Practice

In this tutorial, we will create a program that adds two complex numbers (a1 + ib1) and (a2 + ib2) by utilizing a class.

For example

Input: 4 + i5 and 8 + i9

Here when a1 is equal to 4 and a2 is equal to 8. By adding a1 and a2 together, the result is (8 + 4) which equals 12.

Furthermore, assuming b1 equals 5 and b2 equals 9. When we sum up b1 and b2, the result is (5 + 9) which equals 14.

Output: 9 + i14

Input: 2 + i7 and 10 + i6

Here a1 equals 2 while a2 equals 10. When we sum up a1 and a2, the result is (2 + 10) which equals 12.

Additionally, assuming b1 equals 7 and b2 equals 6. When we sum up b1 and b2, the result is (7 + 6) = 13.

Output: 12 + i13

Class construction

Initially, let's establish a class dedicated to complex numbers. It is evident that a complex number comprises a real component (a1) and an imaginary component (b1) based on observations.

We require two data attributes to signify the complex numbers.

Below is the class structure:

Example


class Complex 
{
	public:
	int real; // To store real part of complex number
	int imaginary; // To store imaginary part of complex number
}

Constructors

Two different constructors are going to be created in order to set the initial values of the attributes within the Complex class. The first one

✅ will be a constructor that doesn't require any parameters.

We require a constructor without parameters to set the initial values of the attributes to zero.

Below is the layout of non-parameterized constructor:

Example


Complex()
{
	real = 0;
	imaginary = 0;
}

✅ Parameterized constructor

We require a parameterless constructor to set the data attributes to the values provided by the main function.

The following is the layout of a parameterized constructor:

Example


Complex(int r, int i)
{
	real = r; // r is initialized during object creation
	imaginary = i; // i is initialized during object creation

}

Algorithm

When performing the addition of two complex numbers, it is necessary to instantiate two instances of the Complex class and assign the respective values to them. Subsequently, a third object should be created to hold the outcome of the addition.

C++ code

Example


// C++ program to Add two complex numbers
#include <bits/stdc++.h>
using namespace std;

class Complex {
public:
    int real; // To store real part of complex number
    int imaginary; // To store imaginary part of complex number

    Complex()
    {
	// Initial values are zero 
        real = 0;
        imaginary = 0;
    }
    Complex(int r, int i)
    {
        real = r; // r is initialized during object creation
        imaginary = i; // i is initialized during object creation
    }

    Complex addComplexNumber(Complex C1, Complex C2)
    {

        Complex res; // result object of complex class

        // adding real part of complex numbers
        res.real = C1.real + C2.real;

        // adding Imaginary part of complex numbers
        res.imaginary = C1.imaginary + C2.imaginary;

        // returning the sum
        return res;
    }
};

// Main Class
int main()
{

    // First Complex number
    Complex C1(4, 5);

    // printing first complex number
    cout << "Complex number 1 : " << C1.real
         << " + i" << C1.imaginary << endl;

    // Second Complex number
    Complex C2(8, 9);

    // printing second complex number
    cout << "Complex number 2 : " << C2.real
         << " + i" << C2.imaginary << endl;

    // for Storing the sum
    Complex C3;

    // calling addComplexNumber() method
    C3 = C3.addComplexNumber(C1, C2);

    // printing the sum
    cout << "Sum of complex number : "
         << C3.real << " + i"
         << C3.imaginary;

    cout << endl
         << endl;
    // Test for second input
    // First Complex number
    Complex A(2, 7);

    // printing first complex number
    cout << "Complex number 1 : " << A.real
         << " + i" << A.imaginary << endl;

    // Second Complex number
    Complex B(10, 6);

    // printing second complex number
    cout << "Complex number 2 : " << B.real
         << " + i" << B.imaginary << endl;

    // for Storing the sum
    Complex C;

    // calling addComplexNumber() method
    C = C.addComplexNumber(A, B);

    // printing the sum
    cout << "Sum of complex number : "
         << C.real << " + i"
         << C.imaginary;
}

Output


Complex number 1 : 4 + i5
Complex number 2 : 8 + i9
Sum of complex number : 12 + i14

Complex number 1 : 2 + i7
Complex number 2 : 10 + i6
Sum of complex number : 12 + i13

Time complexity 
The time complexity is O(1) as we have to call the function addComplexNumber() to add the two complex numbers.

C++ Program To Add Two Complex Numbers Using Class

Class construction

Constructors

Algorithm

Input Required