**Question:** Let \( f(z) = \sin(z) \) be an analytic function on and inside the circle \( |z| = 2 \) in the complex plane. Using Cauchy's integral formula, find the value of the integral\[\oint_C \frac{\sin(z)}{z} \, dz\]where \( C \) is the circle \( |z| = 2 \).

Cauchy's integral formula states that for any function f that is analytic inside and on a simple…

Answered: Question: Let f(x) = sin(z) be an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Question: Let f(x) = sin(z) be an analytic function on and inside the circle |z| = 2 in the complex plane. Using Cauchy's integral formula, find the value of the integral fc sin(²) dz where C' is the circle |z| = 2.