Definition:Additive Group of Complex Numbers

Definition
The additive group of complex numbers $\struct {\C, +}$ is the set of complex numbers under the operation of addition.

Also see

 * Complex Numbers under Addition form Infinite Abelian Group

Thus complex addition is:


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