(a) C is the real axis from - to ∞. -∞ (b) C is a circle of radius 0.5 centered at i. (c) C is a circle of radius 0.5 centered at 2i. (d) C is a circle of radius 0.5 centered at 3i. (e) C is a circle of radius 20 centered at 0.
(a) C is the real axis from - to ∞. -∞ (b) C is a circle of radius 0.5 centered at i. (c) C is a circle of radius 0.5 centered at 2i. (d) C is a circle of radius 0.5 centered at 3i. (e) C is a circle of radius 20 centered at 0.
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
![Please compute the following integrals of the function
\[ I = \int_{C} \frac{1}{(z^2 + 1)(z^2 + 4)} \, dz \]
for the following contours:
(a) \( C \) is the real axis from \( -\infty \) to \( \infty \).
(b) \( C \) is a circle of radius 0.5 centered at \( i \).
(c) \( C \) is a circle of radius 0.5 centered at \( 2i \).
(d) \( C \) is a circle of radius 0.5 centered at \( 3i \).
(e) \( C \) is a circle of radius 20 centered at 0.
Be sure to justify your reasoning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6e2f997-9120-4975-9388-a1bc7e4c3a16%2F7444a154-4e13-498a-a804-0427723df3c3%2F5t5ubs_processed.png&w=3840&q=75)
Transcribed Image Text:Please compute the following integrals of the function
\[ I = \int_{C} \frac{1}{(z^2 + 1)(z^2 + 4)} \, dz \]
for the following contours:
(a) \( C \) is the real axis from \( -\infty \) to \( \infty \).
(b) \( C \) is a circle of radius 0.5 centered at \( i \).
(c) \( C \) is a circle of radius 0.5 centered at \( 2i \).
(d) \( C \) is a circle of radius 0.5 centered at \( 3i \).
(e) \( C \) is a circle of radius 20 centered at 0.
Be sure to justify your reasoning.
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