In each case, determine and classify all the singular points of ƒ(z). If the singular point is a pole, find the order of the pole and the residue of ƒ at each of these poles. (a) f(z) = (b) f(z) = (c) f(z) = (d) ƒ(z) = eiz 1)³ 1 1 + e² 1 - sin z 23 1 z² sin z

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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question b c d

In each case, determine and classify all the singular points of
f(z). If the singular point is a pole, find the order of the pole and the residue of f at each
of these poles.
(a) f(z) =
=
(b) f(z)
=
(c) f(z):
(d) f(z)
=
eiz
2-
1)³
1
1 + e²
1 sin z
z3
1
2² sin z
Transcribed Image Text:In each case, determine and classify all the singular points of f(z). If the singular point is a pole, find the order of the pole and the residue of f at each of these poles. (a) f(z) = = (b) f(z) = (c) f(z): (d) f(z) = eiz 2- 1)³ 1 1 + e² 1 sin z z3 1 2² sin z
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