I put it in exponential form to get $\dfrac{re^{-i \theta}}{re^{i \theta}}$ but I think I'll get $\frac{0}{0}$ which isn't defined and isn't a good enough proof to say it doesn't have a limit.
Find the limit of $\frac{\bar{z}}{z}$ as $z$ goes to $0$.
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sequences-and-series
complex-analysis
limits
convergence
exponential-function
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0You have to decide how $z$ goes to $0$. In terms of $r$ and $x$ for example. Then you can take the limit as usual. – 2012-11-01