Inverse for Complex Addition

Theorem
Each element $z = x + i y$ of the set of complex numbers $\C$ has an inverse element $-z = -x - i y$ under the operation of complex addition:
 * $\forall z \in \C: \exists -z \in \C: z + \left({-z}\right) = 0 = \left({-z}\right) + z$

Proof
From Complex Addition Identity is Zero, the identity element for $\left({\C, +}\right)$ is $0 + 0 i$.

Then:

Similarly for $\left({-x - i y}\right) + \left({x + i y}\right)$.