Complex Addition is Commutative

Theorem
The operation of addition on the set of complex numbers is commutative:
 * $$\forall z, w \in \C: z + w = w + z$$

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


 * $$z = x_1 + i y_1$$
 * $$w = x_2 + i y_2$$

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

Then:

$$ $$ $$