3. Recall that z = x+iy. For each of the given functions, use a result related to the Cauchy- Riemann Equations (sections 21, 23, or 24) to determine where the derivative exists. If it exists, find its value according to the theorem. (i) f(2)=2x+ixy² (ii) g(z) = x³ +iy³ (iii) h(z)= 2²-²
3. Recall that z = x+iy. For each of the given functions, use a result related to the Cauchy- Riemann Equations (sections 21, 23, or 24) to determine where the derivative exists. If it exists, find its value according to the theorem. (i) f(2)=2x+ixy² (ii) g(z) = x³ +iy³ (iii) h(z)= 2²-²
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
105.
![3. Recall that z = 2+iy. For each of the given functions, use a result related to the Cauchy-
Riemann Equations (sections 21, 23, or 24) to determine where the derivative exists. If it
exists, find its value according to the theorem.
(i) f(2)=2x+ixy²
(ii) g(z) = x³ + iy³
(iii) h(2) = 2²-²
(iv) k(z)= ¢ *sin r – ie M cos r](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0db0dd6d-da89-4615-8dcc-00f06ccb1842%2F4b248e76-7d5a-4acd-8a33-fbfa43a1be33%2Fb21spnd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Recall that z = 2+iy. For each of the given functions, use a result related to the Cauchy-
Riemann Equations (sections 21, 23, or 24) to determine where the derivative exists. If it
exists, find its value according to the theorem.
(i) f(2)=2x+ixy²
(ii) g(z) = x³ + iy³
(iii) h(2) = 2²-²
(iv) k(z)= ¢ *sin r – ie M cos r
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