Complex addition is commutative.

$$\forall x,y \in \mathbb{C} : x + y = y + x$$Complex addition is associative.

\(0 + 0i\) is a left-identity element of complex addition.

\(0 + 0i\) is a right-identity element of complex addition.

\(0 + 0i\) is the identity element of complex addition.

Proof unavailable