(a) Find all singularities of the function 1 f(z) = cos(7), and determine the nature of each of these singularities (e.g. removable singularity, pole, essential singularity). Justify all of your steps. (b) Using the Residue Theorem, or otherwise, compute ² (27) dz, Sa COS where C is the positively oriented circle of radius 5 centered at z = 0. State all the theorems that you are using and justify all of your steps.
(a) Find all singularities of the function 1 f(z) = cos(7), and determine the nature of each of these singularities (e.g. removable singularity, pole, essential singularity). Justify all of your steps. (b) Using the Residue Theorem, or otherwise, compute ² (27) dz, Sa COS where C is the positively oriented circle of radius 5 centered at z = 0. State all the theorems that you are using and justify all of your steps.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
5a,b

Transcribed Image Text:Question 5
(a) Find all singularities of the function
f(z)
1
= COS
and determine the nature of each of these singularities (e.g. removable singularity, pole,
essential singularity). Justify all of your steps.
(b) Using the Residue Theorem, or otherwise, compute
1
(27),
COS
dz,
z²
where C is the positively oriented circle of radius 5 centered at z = 0. State all the
theorems that you are using and justify all of your steps.
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