Math 6720 • Applied Complex Variables and Asymptotic Methods

Complete the following:
\begin{enumerate}
\item
(5 pts) Compute the Laurent series expansion about the point \(z=0\) for
\[
f(z)=\frac{1}{(z-i)(z+2)},
\]
in the region \(1<|z|<2\).
\item
(5 pts) Describe the singularities of the function
\[
f(z)=\frac{z+1}{z\sin z}.
\]
\end{enumerate}