i. Let Cr be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) = zo + r exp(it) where r > 0. Explain why ii. Show that √ f(z) √(F(2) 2- 20 f(z) - Zo dz = Cr dz – 2πif (zo) = = f(z) 2- 20 Cr d dz. f(z) - f(zo) 2- 20 dz.

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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i. Let Cr be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) =
zo+rexp(it) where r > 0. Explain why
ii. Show that
f(z)
[1(2) dz- / 1(2) ds.
Se
=
2- 20
| f(z)
2- 20
dz - 2πif (zo) = Sc
ƒ(z) – ƒ (zo)
2 - 20
dz.
Transcribed Image Text:i. Let Cr be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) = zo+rexp(it) where r > 0. Explain why ii. Show that f(z) [1(2) dz- / 1(2) ds. Se = 2- 20 | f(z) 2- 20 dz - 2πif (zo) = Sc ƒ(z) – ƒ (zo) 2 - 20 dz.
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