Definition:Multiplicative Group of Complex Numbers

Definition
The multiplicative group of complex numbers $\left({\C_{\ne 0}, \times}\right)$ is the set of complex numbers without zero under the operation of multiplication.

Also see

 * Non-Zero Complex Numbers under Multiplication form Abelian Group

Thus complex multiplication is:


 * Well-defined on $\C_{\ne 0}$
 * Closed on $\C_{\ne 0}$
 * Associative on $\C_{\ne 0}$
 * Commutative on $\C_{\ne 0}$
 * The identity of $\left({\C_{\ne 0}, \times}\right)$ is $1$
 * Each element of $\left({\C_{\ne 0}, \times}\right)$ has an inverse.