A complex number has two parts: a real part and an imaginary part. One way to write an imaginary number is this: (3.0, 4.0). Here 3.0 is the real part and 4.0 is the imaginary part. Suppose a = (A,Bi) and c = (C,Di).Here are some complex operations:

n Addition: a + c = (A + C, (B + D)i)
n Subtraction: a - c = (A - C, (B - D)i)
n Multiplication: a × c = (A × C - B×D, (A×D + B×C)i)
n Multiplication: (x a real number): x × c = (x×C,x×Di)
n Conjugation: ~a = (A, - Bi)
Define a complex class so that the following program can use it with correct
results:
#include
using namespace std;
#include "complex0.h" // to avoid confusion with complex.h
int main()
{
complex a(3.0, 4.0); // initialize to (3,4i)

complex c;
cout << "Enter a complex number (q to quit):\n";
while (cin >> c)
{
cout << "c is " << c << '\n';
cout << "complex conjugate is " << ~c << '\n';
cout << "a is " << a << '\n";
cout << "a + c is " << a + c << '\n';
cout << "a - c is " << a - c << '\n';
cout << "a * c is " << a * c << '\n';
cout << "2 * c is " << 2 * c << '\n';
cout << "Enter a complex number (q to quit):\n";
}
cout << "Done!\n";
return 0;
}
Note that you have to overload the << and >> operators. Standard C++ already has complex support—rather more extensive than in this example—in a complex header file, so use complex0.h to avoid conflicts. Use const whenever warranted.

Here is a sample run of the program:
Enter a complex number (q to quit):
real: 10
imaginary: 12
c is (10,12i)
complex conjugate is (10,-12i)
a is (3,4i)
a + c is (13,16i)
a - c is (-7,-8i)
a * c is (-18,76i)
2 * c is (20,24i)
Enter a complex number (q to quit):
real: q
Done!
Note that cin >> c, through overloading, now prompts for real and imaginary
parts.