A First Course in Complex Analysis · Problem 2

Integration — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · mobius-transformations

Problem

Complete the picture painted by Proposition 3.1.2 by considering Möbius transformations with

c = 0

. That is, show that

f : \mathbb{C} \to \mathbb{C}

given by

f(z) = \frac{az+b}{d}

is a bijection, with

f^{-1}(z)

given by the formula in Proposition 3.1.2.