Complex Analysis: Theory and Applications · Problem 5.4.14

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · complex-trig-mappings

Problem

Show that the mapping

w = \sin z

(a) maps the

y

axis one-to-one and onto the

v

axis; (b) maps the ray given

\{(x,y) : x = \dfrac{\pi}{2},\, y > 0\}

one-to-one and onto the ray defined by

\{(u,v) : u > 1,\, v = 0\}