Math 6420 • PDE

Consider the bilinear transformation
\[
  \omega=\frac{az+b}{cz+d},\qquad ad-bc\ne0.
\]
\begin{enumerate}
\item[(a)] Show that this transformation maps circles to circles.
\item[(b)] Show that the bilinear transformations form a group.
\item[(c)] In the case \((a,b,c,d)=(1,-i,1,i)\) show that the upper-half plane is mapped on
to the unit disc.
\end{enumerate}