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\begin{document}

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\noindent{\Large{\textsc{Complex Variables\hfill Assignment 3.2  \\ Spring 2020 \hfill Due February 12}}}

\large

\vspace{1cm}


\begin{exercise}
Prove that $\overline{e^z} = e^{\overline{z}}$ for all $z \in \C$.
\end{exercise}

\begin{exercise}
Find every value of $z \in \C$ for which $\overline{e^{iz}} = e^{i \overline{z}}$.
\end{exercise}

\begin{exercise}
Prove that $\log zw = \log z + \log w$, in the sense that both sides take on the same values, for all $z, w \in \C^{\times}$.
\end{exercise}

\begin{exercise}
Give necessary and sufficient conditions on $z, w \in \C^{\times}$ so that $\operatorname{Log}zw= \operatorname{Log}z + \operatorname{Log}w$.
\end{exercise}

\end{document}
