Complex Analysis: Theory and Applications · Problem 8.7.1

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · argument-principle-winding-numbers

Problem

Let

f(z) = z^5 - z

. Find the number of times the image

f(C)

winds around the origin if (a)

C = C_{\frac{1}{2}}(0)

. (b)

C

is the rectangle with vertices

\pm\dfrac{1}{2} \pm 3i

. (c)

C = C_2(0)

. (d)

C = C_{1.25}(i)