. Show that each function is not analytic at any point but is differentiable along the indicated irve(s): ¹) ƒ(z) = x² + y² + 2ixy; x-axis. >) f(z) = 3x²2y² - 6ix²y²; coordinate axes. :) f(z) = x³ + 3xy² - x+i (y³ +3x²y - y); coordinate axes.
. Show that each function is not analytic at any point but is differentiable along the indicated irve(s): ¹) ƒ(z) = x² + y² + 2ixy; x-axis. >) f(z) = 3x²2y² - 6ix²y²; coordinate axes. :) f(z) = x³ + 3xy² - x+i (y³ +3x²y - y); coordinate axes.
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
![6. Show that each function is not analytic at any point but is differentiable along the indicated
curve(s):
(a) f(z) = x² + y² + 2ixy; x-axis.
(b) f(2)= 3x²y² - 6ix2y²; coordinate axes.
(c) f(z) = x³ + 3xy² - x+i (y³ + 3x²y - y); coordinate axes.
(d) f(z)=x²-x+y+i (y²-5y-x); y=x+2.
7. Recalling the definition of the complex exponential function f(z) = e² as
e² = e cos y + ie siny:
(a) Show that f(z) = e² is an entire function.
(b) Show that f'(z) = f(z).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd377aab-d46d-41ac-a49d-b3119dc6fdc9%2F8f3f2426-f10d-405d-905d-7ed78e6a3385%2Fy85ena_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Show that each function is not analytic at any point but is differentiable along the indicated
curve(s):
(a) f(z) = x² + y² + 2ixy; x-axis.
(b) f(2)= 3x²y² - 6ix2y²; coordinate axes.
(c) f(z) = x³ + 3xy² - x+i (y³ + 3x²y - y); coordinate axes.
(d) f(z)=x²-x+y+i (y²-5y-x); y=x+2.
7. Recalling the definition of the complex exponential function f(z) = e² as
e² = e cos y + ie siny:
(a) Show that f(z) = e² is an entire function.
(b) Show that f'(z) = f(z).
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