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.