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QUESTION 3 (3.1) Find the analytic function f(z) = u(x, y) +iv(x, y) given that u(x, y) = sin x coshy and z = x+iy. (3.2) Let f(2)=Ln(z), where -π/2 < Arg(z) 2. Find f'(2) at these points. Show all working. Hence, determine where f is analytic.

QUESTION 3 (3.1) Find the analytic function f(z) = u(x, y) +iv(x, y) given that u(x, y) = sin x coshy and z = x+iy. (3.2) Let f(2)=Ln(z), where -π/2 < Arg(z) 2. Find f'(2) at these points. Show all working. Hence, determine where f is analytic.

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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QUESTION 3 (3.1) Find the analytic function f(z) = u(x, y) + iv(x, y) given that u(x, y) = sin x coshy and z = x+iy. (3.2) Let f(2)=Ln(z), where -π/2 < Arg(2) < π/2. Find f'(z) at these points. Show all working. Hence, determine where f is analytic.
Transcribed Image Text:QUESTION 3 (3.1) Find the analytic function f(z) = u(x, y) + iv(x, y) given that u(x, y) = sin x coshy and z = x+iy. (3.2) Let f(2)=Ln(z), where -π/2 < Arg(2) < π/2. Find f'(z) at these points. Show all working. Hence, determine where f is analytic.
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