Let $U ( n )$ be the group of $n \times n$ unitary complex matrices. Let $P \subset U ( n )$ be the set of all finite order elements of $U ( n )$, that is, $P = \left\{ X \in U ( n ) \mid X ^ { m } = 1 \text{ for some } m \geq 1 \right\}$. Show that $P$ is dense in $U ( n )$.