3z2+z+1 (a) Evaluate using Cauchy's integral formula Sc dz where C is (z²-1)(z+3) the circle |z| = 2.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 53PS
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3z2+z+1
(a) Evaluate using Cauchy's integral formula .
dz where C is
(z²–1)(z+3)
the circle |z| = 2.
(b) Expand the following function in series form:
1
i. f (z) =
for 1 < |z| < 3.
(z-1)(z+3)
4z-1
ii. f(z) =
z4-1
about the point z = 0.
Transcribed Image Text:3z2+z+1 (a) Evaluate using Cauchy's integral formula . dz where C is (z²–1)(z+3) the circle |z| = 2. (b) Expand the following function in series form: 1 i. f (z) = for 1 < |z| < 3. (z-1)(z+3) 4z-1 ii. f(z) = z4-1 about the point z = 0.
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