Complex Analysis: Theory and Applications · Problem 5.2.6

Elementary Functions — Howell & Matthews

Mathematics — Complex Analysis · complex-logarithm-analyticity

Problem

Show that

f(z) = \dfrac{\mathrm{Log}(z+5)}{z^2 + 3z + 2}

is analytic everywhere except at the points

-1

-2

, and on the ray

\{(x,y) : x \leq -5,\ y = 0\}