Define a class for complex numbers. A complex number is a number of

the form a + b*i

where, for our purposes, a and b are numbers of type double, and i is a

number that represents the quantity . Represent a complex number

as two values of type double. Name the member variables real and

imaginary. (The variable for the number that is multiplied by i is the one

called imaginary.) Call the class Complex.

Include a constructor with two parameters of type double that can be used

to set the member variables of an object to any values. Also include a

constructor that has only a single parameter of type double; call this

parameter real_part and define the constructor so that the object will be

initialized to real_part + 0*i. Also include a default constructor that

initializes an object to 0 (that is, to 0 + 0*i). Overload all of the following

operators so that they correctly apply to the type Complex: ==, +, − , *, >>, and <<. You should write a test program to test your class.

Hints: To add or subtract two complex numbers, you add or subtract the

two member variables of type double. The product of two complex

numbers is given by the following formula:

(a + b*i)*(c + d*i) == (a*c − b*d) + (a*d + b*c)*i

In the interface file, you should define a constant i as follows:

const Complex i(0, 1);

This defined constant i will be the same as the i discussed earlier.

delete p;