Complex Analysis: Theory and Applications · Problem 17

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · complex-definite-integrals-square-root

Problem

Let

z^{\frac{1}{2}}

be the principal branch of the square root function. (a) Evaluate

\int_C \frac{1}{2z^{\frac{1}{2}}}\,dz

, where

C

is the line segment joining

9

3+4i

. (b) Evaluate

\int_C z^{\frac{1}{2}}\,dz

, where

C

is the right half of the circle

C_2^+(0)

joining

-2i

2i