Description

Question

This assignment will test your programming skills in C++ as well as your understanding about operator overloading and friend functions. Here, you will be required to develop a simple mathematical application which will be able to perform the normal mathematical operations ( i.e. add, subtract, multiply and divide ) on complex numbers.

For those who are unfamiliar with complex numbers, kindly refer to the article provided by the link below which gives a very clear explanation on this topic.

https://www.mathsisfun.com/numbers/complex-numbers.html

Briefly, a complex number is a number which contains a real and imaginary part and is written in the form a + bi where a is the real part of the complex number and bi the imaginary part.  An example of an imaginary number is 2 + 3i. i has the special characteristic that i2 = -1.

Thus, if num1 and num2 are both complex numbers and num1 = 3 + 4i and num2 = 3 – 4i, then the following should be observed and produced by your program:

(a)    num1 + num2 = 6

(b)   num1 – num2 = 8i

(c)    num1 * num2 = 25

(d)   num1 / num2 = 0.04(-7+24i)

Note: When an operation acts on two complex numbers, it is possible that the results can be either a number consisting only of a real part, an imaginary part or both )

In this assignment, you will be specifically required to ensure that the following are included in your program :

(a)      You need to create the appropriate class to represent complex numbers. The complex numbers should consist of a real and imaginary part and both the real and imaginary parts of the number should be declared as floating point numbers.

(b)     You need to overload the four common mathematical operators which act on complex numbers i.e. the multiplication, division, addition and subtraction operators. The operators should act on the complex numbers as explained above.

(c)      You need to write an appropriate function to print out the results of the operations performed and the results should be printed either in the form a + bi or a + ib.  

(d)     You need to write a main program using suitable test complex numbers to confirm that your program works correctly.

(e)      Ensure that proper and adequate comments is provided in your program to explain how your program works. Make sure that you indent your programs appropriately and use meaningful names for attributes and methods.

It is anticipated that your program should only be between 100 to 150 lines ( without comments ) if you plan correctly. You will be required to submit the completed program with the output using test results to the exam department before 5.00pm on Wednesday 12th February 2020. You will also be required to mail to me a copy of your source code to enable me to perform further checking.