Math 6420 • PDE

\begin{enumerate}
\item[(a)] Show that the transformation \(w=2z+1/z\) maps the unit circle conformally onto
the ellipse
\[
  \left(\frac{u}{3}\right)^2+v^2=1.
\]
Here \(w=u+iv\).

\item[(b)] Find the M\"obius transformation that takes the points \(z_1=0\), \(z_2=1\),
\(z_3=-i\) into \(w_1=1\), \(w_2=0\), \(w_3=i\).
\end{enumerate}