Let R be the rectangle with vertices -1-i, 8i, 8+i, -1+i. Use residues to evaluate the following integral. 1 L (²1 + 2 2² 3 R 3i dz

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let \( R \) be the rectangle with vertices \(-1 - i, 8 - i, 8 + i, -1 + i\). Use residues to evaluate the following integral.

\[
\oint_{R} \left( \frac{2}{z} + \frac{1}{z - 3} - \frac{3i}{z - 7} \right) dz
\]
Transcribed Image Text:Let \( R \) be the rectangle with vertices \(-1 - i, 8 - i, 8 + i, -1 + i\). Use residues to evaluate the following integral. \[ \oint_{R} \left( \frac{2}{z} + \frac{1}{z - 3} - \frac{3i}{z - 7} \right) dz \]
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