Question

A complex number is a number in the form of a + bi, where a and b are real numbers and i is the square root of negative 1.

Design and create a class called Complex for representing complex numbers. This class should have two attributes, a and b, which represent the parts of the complex number. This class should overload the +,-,*,/,++ and -- operators (both prefix and suffix) to perform basic complex number calculations according to the following formulas:

a + bi + c + di = (a+c) + (b+d)i

a + bi - (c + di) = (a-c) + (b - d)i

(a + bi)*(c + di) = (ac - bd) + (bc + ad)i

(a + bi)/(c + di) = (ac + bd)/(c^2 + d^2) + (bc - ad)i/(c^2 + d^2)

For example, 5 + 3i + 6 + 2i = 11 + 5i

(5+3i)*(6+2i) = (5*6 - 3*2) + (3*6 + 5*2)i = 24 + 28i

++ and -- should simply add or subtract one to the real part (a)

Provide three constructors Complex (a,b), Complex (a) and Complex().

Complex() gives a number with a and b = 0, Complex(a) gives a number with a set but b=0, and Complex(a,b) sets both values. Your class should also have getRealPart() and getImaginaryPart() methods for returning the value of a and b respectively, as well as a method that returns the string representation of the number (to be used for displaying purposes later).

For the main program that will use the Complex class, prompt the user for how many complex numbers they wish to use. Then create an array of Complex numbers and prompt the user for values a and b for the entire array.

Now display the entire array and ask the user which number they would like to work with. Once the user has selected a number, ask the user if they would like to do a unary or binary operation. If they answer unary, prompt for ++prefix, postfix++, --prefix, postfix-- and then what number to store the result in. Then perform that operation. If they say they want to perform a binary operation, prompt for an operation (+,-,*,/) and then the second operand. Lastly, ask them in which number they wish to store the result. Perform the calculation and put the result where they told you to put it. In your code, use overloaded operators to do the work. This means you should implement overloaded operators of +,-,*,/,++,--(pre and post) and =(assignment).

If users have the following list of numbers

1) 5 + 3i

2) 2 - 4i

3) 3 + 5i

4) quit

and they select 1, then prompt them for

1) unary

2) binary

if they select 2, then ask user what type of operation

1) +

2) –

3) *

4) /

if they enter +, then redisplay the numbers and prompt them for the second operand

1) 5 + 3i

2) 2 - 4i

3) 3 + 5i

4) quit

If they enter 2, then ask them for where to store the result. Suppose they enter 3 for the result. Then you want to do number 1 + number 2 and store the result in element 3.

Example: (5+3i) + (2 - 4i) and store the result in number 3

program should continue with this in a menu until the user selects quit.

The program should deal with the divide by zero error by throwing an exception in the divide overload, catching it in the main body and outputting an appropriate error message, after which you can let the program terminate. Meaning, use a try/catch block to throw an error and end the program for divison by 0.