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: