Recall the polar form of the Cauchy-Riemann Equations: 1 ƏV 1 ƏU r +0. r d0 av ar dr -i0 (0 + i). Let f(z) = z45. Use av dr The derivative can be recovered by f'(z) : the polar form of C-R equations to prove that f has a derivative at all non-zero points and show that f'(z) = 45z44. = e ar

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Recall the polar form of the Cauchy-Riemann Equations:
1 ƏV
1 ƏU
r +0.
r d0
av
ar
dr
-i0 (0 + i). Let f(z) = z45. Use
av
dr
The derivative can be recovered by f'(z) :
the polar form of C-R equations to prove that f has a derivative at all non-zero
points and show that f'(z) = 45z44.
= e
ar
Transcribed Image Text:Recall the polar form of the Cauchy-Riemann Equations: 1 ƏV 1 ƏU r +0. r d0 av ar dr -i0 (0 + i). Let f(z) = z45. Use av dr The derivative can be recovered by f'(z) : the polar form of C-R equations to prove that f has a derivative at all non-zero points and show that f'(z) = 45z44. = e ar
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