$z_{n} = r_{n}e^{i\theta_{n}}$ and $z = re^{i\theta}$. If $z_{n} \rightarrow z$ then $r_{n} \rightarrow r$ and $\theta_{n} \rightarrow \theta$.
Limit of argz and r
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complex-analysis
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0I was trying this problem but couldn't solve it. could someone help? Thanks. – 2012-09-18
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1$\theta_n \to \theta$ will hold only if $z \ne 0$, in this case, use that $z \mapsto \sqrt{(\Re z)^2 + (\Im z)^2}$ and $z \mapsto \arctan\frac{\Im z}{\Re z}$ are continuous – 2012-09-18