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3. If C is the unit circle in the complex plane C, and f(2)= =², show that f(z) dz = 0 using two ways: (a) by a direct multivariable integration by writing == x+iy and suitably parametrizing C, and (b) using a relevant theorem.

3. If C is the unit circle in the complex plane C, and f(2)= =², show that f(z) dz = 0 using two ways: (a) by a direct multivariable integration by writing == x+iy and suitably parametrizing C, and (b) using a relevant theorem.

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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3. If C is the unit circle in the complex plane C, and f(2)= =², show that (2) dz = 0 using two ways: (a) by a direct multivariable integration by writing = x+iy and suitably parametrizing C, and (b) using a relevant theorem.
Transcribed Image Text:3. If C is the unit circle in the complex plane C, and f(2)= =², show that (2) dz = 0 using two ways: (a) by a direct multivariable integration by writing = x+iy and suitably parametrizing C, and (b) using a relevant theorem.
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