8.) Consider the contour C in the complex plane consisting of the portion from z = 1 to z = 2+ i. of the unit circle from z = -i to z = 1 followed by the line segment iR 2+i -2 R 1 Compute the following contour integrals directly by the definition. Then verify your answer by finding an appropriate anti-derivative and eval- uating at the endpoints of the countour. a.) Se b.) C - C2 2 dz dz (Your final answer should involve Arctan(1/2) which is equivalent to the usual real-valued version of arctangent.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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8.) Consider the contour C in the complex plane consisting of the portion
from z = 1 to z = 2+ i.
of the unit circle from z = -i to z = 1 followed by the line segment
iR
2+i
-2
R
1
Compute the following contour integrals directly by the definition. Then
verify your answer by finding an appropriate anti-derivative and eval-
uating at the endpoints of the countour.
a.) Se
b.)
C
-
C2
2 dz
dz (Your final answer should involve Arctan(1/2) which is
equivalent to the usual real-valued version of arctangent.)
Transcribed Image Text:8.) Consider the contour C in the complex plane consisting of the portion from z = 1 to z = 2+ i. of the unit circle from z = -i to z = 1 followed by the line segment iR 2+i -2 R 1 Compute the following contour integrals directly by the definition. Then verify your answer by finding an appropriate anti-derivative and eval- uating at the endpoints of the countour. a.) Se b.) C - C2 2 dz dz (Your final answer should involve Arctan(1/2) which is equivalent to the usual real-valued version of arctangent.)
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