Complex Multiplication is Commutative

Theorem
$$\forall z_1, z_2 \in \mathbb{C}: z_1 z_2 = z_2 z_1$$.

Proof
From the definition of complex numbers, we define the following:


 * $$z_1 = x_1 + \imath y_1$$
 * $$z_2 = x_2 + \imath y_2$$

where $$\imath = \sqrt {-1}$$ and $$x_1, x_2, y_1, y_2 \in \mathbb{R}$$.

Then:

$$ $$ $$ $$ $$