A First Course in Complex Analysis · Problem 14

Integration — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · mobius-transformations

Problem

Find Möbius transformations satisfying each of the following. Write your answers in standard form, as

\frac{az+b}{cz+d}

. ((a))

1 \to 0,\ 2 \to 1,\ 3 \to \infty

Answer.

\frac{-z+1}{z-3}

((b))

1 \to 0,\ 1+i \to 1,\ 2 \to \infty

Answer.

\frac{(i-1)z+1-i}{iz-2i}

((c))

0 \to i,\ 1 \to 1,\ \infty \to -i

Answer.

\frac{iz-1}{-z+i}