Consider the two arcs of the unit circle (note that C1 U C2 form the boundary of the unit circle): C1 : - <0

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.4: Analytic Proofs
Problem 32E
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Consider the two arcs of the unit circle (note that C1 U C, form
the boundary of the unit circle):
C1 : -5<0ST
C2 : T <O<
Perform the following 4 integrals:
2
i. So, dz/z
ii. Sc, dz/z
iii. fiel=1 dz/z
iv. fiel=1 zdz
v. Explain how the 4 integrals are related by the Cauchy-Goursat
theorem.
Transcribed Image Text:Consider the two arcs of the unit circle (note that C1 U C, form the boundary of the unit circle): C1 : -5<0ST C2 : T <O< Perform the following 4 integrals: 2 i. So, dz/z ii. Sc, dz/z iii. fiel=1 dz/z iv. fiel=1 zdz v. Explain how the 4 integrals are related by the Cauchy-Goursat theorem.
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