(3) Sketch the points (−1+ ei)¹/5 and (-1 - ei)¹/5 for € "small". Based on your sketch, explain why it's not possible that z¹/5 is differentiable at z = -1.
(3) Sketch the points (−1+ ei)¹/5 and (-1 - ei)¹/5 for € "small". Based on your sketch, explain why it's not possible that z¹/5 is differentiable at z = -1.
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) Sketch the points (−1+ ei)¹/5 and (−1 – ei)¹/5 for € "small". Based on your sketch, explain why it's not
possible that z¹/5 is differentiable at z = -1.
(4) Sketch the set {z¹/5 | z € C \ (-∞, 0]} and sketch the set {z¹/5 | z € C \ 0} .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5edd3292-9e27-4357-b238-81fd874a8a41%2F89b2b2b7-ce16-4cfe-89ae-d32af0ff7600%2Fb7vnx5l_processed.png&w=3840&q=75)
Transcribed Image Text:(3) Sketch the points (−1+ ei)¹/5 and (−1 – ei)¹/5 for € "small". Based on your sketch, explain why it's not
possible that z¹/5 is differentiable at z = -1.
(4) Sketch the set {z¹/5 | z € C \ (-∞, 0]} and sketch the set {z¹/5 | z € C \ 0} .
![def
=
=
Exercise 1. Recall we defined in the lectures log(z) log |z|+iArg(z) for z ‡ 0, and for a € C, we had za
for z 0 (both functions are well defined, but they are analytic on C\ (-∞, 0]).
ea log(z)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5edd3292-9e27-4357-b238-81fd874a8a41%2F89b2b2b7-ce16-4cfe-89ae-d32af0ff7600%2Fz854nwg_processed.png&w=3840&q=75)
Transcribed Image Text:def
=
=
Exercise 1. Recall we defined in the lectures log(z) log |z|+iArg(z) for z ‡ 0, and for a € C, we had za
for z 0 (both functions are well defined, but they are analytic on C\ (-∞, 0]).
ea log(z)
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