dz; |z – i| = 1 (z – i)3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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using cauchy-intergral fomulA

11.
dz; |z – i| = 1
(z – i)3
Transcribed Image Text:11. dz; |z – i| = 1 (z – i)3
Expert Solution
Step 1

We have to use the Cauchy integral formula to evaluate the following integral

 ez2z-ι3dz over the region z-ι=1.

We know that z=x+ιy where x, y. So we get, 

z-ι=x+ιy-ι=x+ιy-1

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