Definition:Additive Group of Complex Numbers

Definition
The additive group of complex numbers $\left({\Q, +}\right)$ is the set of complex numbers under the operation of addition.

Also see

 * Complex Numbers under Addition form Abelian Group

Thus complex addition is:


 * Well-defined on $\C$
 * Closed on $\C$
 * Associative on $\C$
 * Commutative on $\C$
 * The identity of $\left({\C, +}\right)$ is $0$
 * Each element of $\left({\C, +}\right)$ has an inverse.