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;
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