2+2 -dz; = z²(z-1-i) (a) || = 1, (b) | - 1 - i = 1 (5) f 1 fc = 23 ( 2 - 4) (a) | = 1, (b) |z – 2 = 1 -dz;
2+2 -dz; = z²(z-1-i) (a) || = 1, (b) | - 1 - i = 1 (5) f 1 fc = 23 ( 2 - 4) (a) | = 1, (b) |z – 2 = 1 -dz;
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 24E
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Question
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Evaluate contour

Transcribed Image Text:2+2
-dz;
z²(z - 1 - i)
(a) || = 1,
(b) | 2 - 1 - i = 1
(5) f
1
fo
z³(z - 4)
(a) || = 1,
(b) | = 2 = 1
=
- dz;
Expert Solution

Step 1: ''Introduction to the solution''
5) a) Let
Cleary, g is analytic inside and on C.
Then, we can apply the Cauchy Integral theorem for the above integral.
Cauchy Integral's theorem: Let be an analytic function inside and on a closed contour C and
IntC, being the interior of C. Then,
Then,
Now,
Now,using this value in (3), we get,
(b) Let being analytic inside and on C:
Then, by Cauchy's Integral theorem,
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