Complex Number Calculation Formulas:
   (a + bi) ÷ (c + di) = (ac + bd)/(c² + (d²) + ((bc - ad)/(c² + d²))i;
   (a + bi) × (c + di) = (ac - bd) + (ad + bc)i;
   (a + bi) + (c + di) = (a + c) + (b + d)i;
   (a + bi) - (c + di) = (a - c) + (b - d)i;

Examples:

   (7 + 2i) + (4 - 3i) = 11 - i;
   (7 + 2i) - (4 - 3i) = 3 + 5i;
   (7 + 2i) × (4 - 3i) = 34 - 13i;
   (7 + 2i) ÷ (4 - 3i) = 22/25 + (29/25)i;


The Complex Number System:

The Number i is defined as i = √-1. For Example, we know that equation x2 + 1 = 0 has no solution, with number i, we can define the number as the solution of the equation. So the root of negative number √-n can be solved as √-1 * n = √n i, where n is a positive real number. The complex numbers are in the form of a real number plus multiples of i. For example, complex number A + Bi is consisted of the real part A and the imaginary part B, where A and B are positive real numbers. When A = 0, the number Bi then is called as a pure imaginary number.