(a) Find all singularities of the function f(z) = sin cos(z-7) (z-37) (z+4i)²¹ and determine the nature of each of these singularities (e.g. removable singularity, pole, essential singularity). Justify all of your steps.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 44E
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a)

(a) Find all singularities of the function
f(z) =
=
sin cos(z-7)
(z − 3) (z+4i)²¹
and determine the nature of each of these singularities (e.g. removable singularity, pole,
essential singularity). Justify all of your steps.
Transcribed Image Text:(a) Find all singularities of the function f(z) = = sin cos(z-7) (z − 3) (z+4i)²¹ and determine the nature of each of these singularities (e.g. removable singularity, pole, essential singularity). Justify all of your steps.
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