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\lhead{\bf Complex Analysis (MAA 4402 / 5404)}
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\rhead{Due Wednesday 2/26}
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%\noindent\emph{Answers should be submitted on a separate piece of paper. You need not attach this page, although if you do, then you will have the questions when your work is returned. Work which is sloppy or messy or that which is not written in a clear and coherent fashion will be marked down.}

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\begin{enumerate}

\Problem Apply the theorem from Section 23 of the book to verify that the function
\[
	f(z)=\cosh x\cos y + i\sinh x\sin y
\]
is entire.

\Problem Let $f$ be an entire function for which $f(z)=z$ whenever $\textrm{Arg}(z)=\pi/3$. Determine, with justification, the function $f$. (There are theorems in Section 28 that are helpful here.)

\Problem For which complex numbers $z$ is it true that $|e^{-3z}|<8$?

\end{enumerate}


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