(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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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.
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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