Units of Field of Complex Numbers form Group

Theorem

$\C^\times = \C \setminus \set 0$

where $\C^\times$ denotes the group of units of $\C$.

Proof

By Complex Numbers form Field, $\C$ is a field.

From Group of Units of Field it follows that:

$\C^\times = \C \setminus \set 0$

$\blacksquare$