Math 6720 • Applied Complex Variables and Asymptotic Methods

\begin{enumerate}
\item
(10 points) Prove that if both \(f(z)\) and \(\overline{f(z)}\) are holomorphic in a simply connected
domain then \(f\) is a constant function in that domain.

\item
(10 points) Identify, with justification, the branch points of the function
\[
f(z)=\frac{1}{\sqrt{(z+1)(z-i)}}.
\]
Propose a corresponding branch cut.
\end{enumerate}