Complex Analysis: Theory and Applications · Problem 9.3.13

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · conformal-mapping-exercise

Problem

Find the branch of

w = (z^2 + 1)^{\frac{1}{2}}

that maps the right half-plane

\operatorname{Re}(z) > 0

onto the right half-plane

\operatorname{Re}(w) > 0

slit along the segment

0 < u \leq 1

v = 0