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(4) If f(2) is an analytic function of z = r + iy, prove that |f(2)[* = 4 |f'(2)|². %3D dy

(4) If f(2) is an analytic function of z = r + iy, prove that |f(2)[* = 4 |f'(2)|². %3D dy

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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Subject:Lagrangian theorem Kindly solve these Q4,5,6 .Give it a try . KINDLY SEND ME AS SOON AS POSSIBLE.Thank you !!
(4) If f(2) is an analytic function of z = r + iy, prove that d+ ) \f(2))° = 4|f'(2)/* . (5) Evaluate |2|Zdz, where C consists of the semicircle {2| |2| = 1, Im z 2 0} and the line segment -1<r<1. (6) Determine F'(-3i) if F(a) = | 522 - 4z + 3 dz, 2 - a where C is the ellipse 16a2 + 9y? = 144.
Transcribed Image Text:(4) If f(2) is an analytic function of z = r + iy, prove that d+ ) \f(2))° = 4|f'(2)/* . (5) Evaluate |2|Zdz, where C consists of the semicircle {2| |2| = 1, Im z 2 0} and the line segment -1<r<1. (6) Determine F'(-3i) if F(a) = | 522 - 4z + 3 dz, 2 - a where C is the ellipse 16a2 + 9y? = 144.
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