Units of Field of Complex Numbers form Group
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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:
- $\C^\times = \C \setminus \set 0$
$\blacksquare$