Let F be the function defined by F (2) (Log(z − 3i) — Log(z +3i)), 6i where Log denotes the principal complex logarithm function. = i. Describe the largest region R on which the function F is holomorphic. ii. Show that F is an antiderivative for the function f: R→ C defined by

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Let F be the function defined by
F(z)
=
6i
(Log(z − 3i) — Log(z +3i)),
where Log denotes the principal complex logarithm function.
i. Describe the largest region R on which the function F is holomorphic.
ii. Show that F is an antiderivative for the function f : R→ C defined by
1
z²+9
f(z) =
for all
ZER.
Transcribed Image Text:Let F be the function defined by F(z) = 6i (Log(z − 3i) — Log(z +3i)), where Log denotes the principal complex logarithm function. i. Describe the largest region R on which the function F is holomorphic. ii. Show that F is an antiderivative for the function f : R→ C defined by 1 z²+9 f(z) = for all ZER.
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