Math 6720 • Applied Complex Variables and Asymptotic Methods

\begin{enumerate}
\item
(10 pts) Compute the Laurent series expansion about the point \(z=0\) for
\[
f(z)=\frac{i+2}{(z+i)(z-2)},
\]
in the region \(1<|z|<2\).
\item
(10 pts) Discuss the type of singularity (removable, pole and order, essential, branch,
cluster). If the type is a pole give the strength of the pole, and give the nature
(isolated or not). Include the point at infinity.
\[
f(z)=\frac{e^{2z}-1}{z}
\]
\end{enumerate}