A First Course in Complex Analysis · Problem 17

Integration — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · mobius-transformations

Problem

Describe the image of the region under the transformation: ((a)) The disk

|z| < 1

under

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

. ((b)) The quadrant

x > 0

y > 0

under

w = \frac{z-i}{z+i}

. ((c)) The strip

0 < x < 1

under

w = \frac{z}{z-1}