Possible Duplicate:
Limit of argz and r
$z_{n} = r_{n}e^{i\theta_{n}}$ and $z = re^{i\theta}$. If $z_{n} \rightarrow z$ then $r_{n} \rightarrow r$ and $\theta_{n} \rightarrow \theta$. $z_{n},z \in G = C - \{z:z \leq 0\}$ and $ - \pi < \theta, \theta_{n} < \pi$.