Math 6720 • Applied Complex Variables and Asymptotic Methods

Complete the following:
\begin{enumerate}
\item
(5 pts) Prove that if both \(f(z)\) and \(\overline{f(z)}\) are analytic in some domain, then \(f\) is the
constant function in that domain.
\item
(5 pts) Identify, with justification, the branch points of the function
\[
f(z)=\frac{1}{\sqrt{z+1}}
\]
and propose a corresponding branch cut.
\end{enumerate}