Question 8.4: Prove that the angle between two curves C1 and C2 passing th...

Prove that the angle between two curves $C_{1}$ and $C_{2}$ passing through the point $z_{0}$ in the $z$ plane [see Figs. 8-1 and 8-2, page 243] is preserved [in magnitude and sense] under the transformation $w=f(z)$, i.e., the mapping is conformal, if $f(z)$ is analytic at $z_{0}$ and $f^{\prime}\left(z_{0}\right) \neq 0$.