Show that the functions below are meromorphic; that is, the only singu- larities in the finite z plane are poles. Determine the location, order and strength of the poles. (d) (a) e² Z z4+2 z4 (b) tan z 1 2πi (c) Z sin² z w dw (e) fc (w² - 2) (w - z) C is the unit circle centered at the origin. First find the function for |z| < 1, then analytically continue the function to [z] ≥ 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
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3. Show that the functions below are meromorphic; that is, the only singu-
larities in the finite z plane are poles. Determine the location, order and
strength of the poles.
(a)
e²
(d)
Z
z4+2
1
z4
(b) tan z
1
(e)
Z
sin² z
dw
$c (w² -2)(w - z)
2лi
(c)
C is the unit circle centered at the origin. First find the function for |z| < 1,
then analytically continue the function to |z| ≥ 1.
Transcribed Image Text:3. Show that the functions below are meromorphic; that is, the only singu- larities in the finite z plane are poles. Determine the location, order and strength of the poles. (a) e² (d) Z z4+2 1 z4 (b) tan z 1 (e) Z sin² z dw $c (w² -2)(w - z) 2лi (c) C is the unit circle centered at the origin. First find the function for |z| < 1, then analytically continue the function to |z| ≥ 1.
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