Inverse for Complex Addition

Theorem
Let $z = x + i y \in \C$ be a complex number.

Let $-z = -x - i y \in \C$ be the negative of $z$.

Then $-z$ is the inverse element of $z$ 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 $\left({-x - i y}\right) + \left({x + i y}\right)$.