Complex Analysis: Theory and Applications · Problem 5.2.11

Elementary Functions — Howell & Matthews

Mathematics — Complex Analysis · complex-logarithm-branch-construction

Problem

Construct branches of

f(z) = \log(z+2)

that are analytic at all points in the plane except at points on the following rays. ((a))

\{(x,y) : x \geq -2,\ y = 0\}

. ((b))

\{(x,y) : x = -2,\ y \geq 0\}

. ((c))

\{(x,y) : x = -2,\ y \leq 0\}