10.5.17 Conformal mappings
Problem:
Find the image of domain
\[
D=\{|z|>1\} \cup\{|z| \leq 1, \operatorname{Im} z>0\} \backslash\{z=i t,-2 \leq t<-1\}
\]
when mapped by the Joukowsky transform:
\[
f(z)=\frac{1}{2}\left(z+\frac{1}{z}\right)
\]