2. Let f(z) = (2-S₁)(z-S₂)(z-Sn), where S1, S2,..., Sn E C. If y is a positively oriented simple closed contour enclosing every Si in its interior, dz prove that (2) = 0.
2. Let f(z) = (2-S₁)(z-S₂)(z-Sn), where S1, S2,..., Sn E C. If y is a positively oriented simple closed contour enclosing every Si in its interior, dz prove that (2) = 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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![2. Let f(z) = (z-S₁) (z-S₂)(z-Sn), where S₁, S2,..., Sn E C. If y
is a positively oriented simple closed contour enclosing every Si in its interior,
dz
prove that
= 0.
f(z)
Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e4d9fcf-6374-447f-8b72-118314acdae6%2Fe9b767ea-61bd-4529-b120-baa5c346af36%2Fimxzyfk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let f(z) = (z-S₁) (z-S₂)(z-Sn), where S₁, S2,..., Sn E C. If y
is a positively oriented simple closed contour enclosing every Si in its interior,
dz
prove that
= 0.
f(z)
Y
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