Complex Analysis: Theory and Applications · Problem 6.3.1

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · cauchy-goursat-theorem

Problem

Determine the domain of analyticity for the following functions and evaluate

\displaystyle\int_{C_1^+(0)} f(z)\,dz

. (a)

f(z) = \dfrac{z}{2z^2+1}

. (b)

f(z) = \dfrac{1}{z^2+2z+2}

. (c)

f(z) = \tan z

. (d)

f(z) = \operatorname{Log}(z+5)