8.) Consider the contour C in the complex plane consisting of the portion of the unit circle from z = -i to z = 1 followed by the line segment from 1 to 2=2+1. iR 2+1 R 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.) /20 2² dz b.)dz (Your final answer should involve Arctan(1/2) which is equivalent to the usual real-valued version of arctangent.)
8.) Consider the contour C in the complex plane consisting of the portion of the unit circle from z = -i to z = 1 followed by the line segment from 1 to 2=2+1. iR 2+1 R 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.) /20 2² dz b.)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
Problem 1RQ
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Question
*Should get the same answer for both the contour

Transcribed Image Text:8.) Consider the contour C in the complex plane consisting of the portion
of the unit circle from z = -i to z = 1 followed by the line segment
from 1 to 2=2+1.
iR
2+1
R
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.)
/20
2² dz
b.)dz (Your final answer should involve Arctan(1/2) which is
equivalent to the usual real-valued version of arctangent.)
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