3. (a) (b) (c) Compute the following complex line integrals: dz where 1 is the unit circle (traversed counterclockwise). 25 dz where 72 is the quarter-circle centered at 0, starting at 1 and ending at i. 72 25 dz where ya is the straight line segment starting at 1 and ending at i. Ys
3. (a) (b) (c) Compute the following complex line integrals: dz where 1 is the unit circle (traversed counterclockwise). 25 dz where 72 is the quarter-circle centered at 0, starting at 1 and ending at i. 72 25 dz where ya is the straight line segment starting at 1 and ending at i. Ys
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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Transcribed Image Text:3. Compute the following complex line integrals:
(a) \(\oint_{\gamma_1} \frac{1}{z^2} \, dz\) where \(\gamma_1\) is the unit circle (traversed counterclockwise).
(b) \(\int_{\gamma_2} z^5 \, dz\) where \(\gamma_2\) is the quarter-circle centered at 0, starting at 1 and ending at \(i\).
(c) \(\int_{\gamma_3} z^5 \, dz\) where \(\gamma_3\) is the straight line segment starting at 1 and ending at \(i\).
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