Complex Numbers under Addition form Infinite Abelian Group

Theorem
Let $\C$ be the set of complex numbers.

The structure $\struct {\C, +}$ is an infinite abelian group.

Proof
From Complex Numbers under Addition form Group, $\struct {\C, +}$ is a group.

Then:
 * Complex Addition is Commutative

and:
 * Complex Numbers are Uncountable.