Complex Analysis: Theory and Applications · Problem 6.3.4

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · cauchy-goursat-theorem

Problem

Find

\displaystyle\int_C (z^2 - z)^{-1}\,dz

for (a) circle

C = C_2^+(1) = \{z : |z-1| = 2\}

having positive orientation. (b) circle

C = C_{\frac{1}{2}}^+(1) = \{z : |z-1| = \frac{1}{2}\}

having positive orientation.