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