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.