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## Complex Numbers Division Calculator

 +   i ÷ +   i = +   i

## Complex Numbers Multiplication Calculator

 +   i × +   i = +   i

 +   i + +   i = +   i

## Complex Numbers Subtraction Calculator

 +   i - +   i = +   i

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.