Complex Analysis: Theory and Applications · Problem 9.2.12

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · bilinear-transformations

Problem

S_1(z) = \dfrac{z-2}{z+1}

and

S_2(z) = \dfrac{z}{z+3}

, find

S_1\!\left(S_2(z)\right)

and

S_2\!\left(S_1(z)\right)