Math 6720 • Applied Complex Variables and Asymptotic Methods

Complete the following:
\begin{enumerate}
\item
(8 pts) Suppose that \(f\) is analytic in some domain with purely real values. Show
that \(f\) is the constant function.
\item
(12 pts) Consider two entire functions with no zeros and having a ratio equal to
unity at infinity. Use Liouville's Theorem to show that they are in fact the same
function. Justify all your steps, including satisfying the assumptions of Liouville's
theorem.
\end{enumerate}