Subtraction of Complex Numbers

Theorem
Let $z_1 := a_1 + i b_1$ and $z_2 := a_2 + i b_2$ be complex numbers.

The subtraction operation on $z_1$ and $z_2$ is:
 * $z_1 - z_2 = \paren {a_1 - a_2} + i \paren {b_1 - b_2}$