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et C be the contour starting at z = −2, going around the circle |z| = 2 erclockwise, and ending out at z = −2 again. Find the value of Jo Log(z) Z dz

et C be the contour starting at z = −2, going around the circle |z| = 2 erclockwise, and ending out at z = −2 again. Find the value of Jo Log(z) Z dz

Advanced Engineering Mathematics
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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Let \( C \) be the contour starting at \( z = -2 \), going around the circle \( |z| = 2 \) counterclockwise, and ending out at \( z = -2 \) again. Find the value of \[ \int_{C} \frac{\log(z)}{z} \, dz \]
Transcribed Image Text:Let \( C \) be the contour starting at \( z = -2 \), going around the circle \( |z| = 2 \) counterclockwise, and ending out at \( z = -2 \) again. Find the value of \[ \int_{C} \frac{\log(z)}{z} \, dz \]
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Step 1: According to this given question

To evaluate the given contour integral

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