7.4. For each of the following functions, determine the set of points at which it is (i) differentiable and (ii) analytic. Find the derivative where it exists. (a). f(z) = (x³ + 3xy² − 3x) +i(y³ + 3x²y - 3y), (b). f(z) = 6z² - 2z - 4i|z|², (c). f(z) = (3x² + 2x - 3y² - 1) + i(6xy + 2y),
7.4. For each of the following functions, determine the set of points at which it is (i) differentiable and (ii) analytic. Find the derivative where it exists. (a). f(z) = (x³ + 3xy² − 3x) +i(y³ + 3x²y - 3y), (b). f(z) = 6z² - 2z - 4i|z|², (c). f(z) = (3x² + 2x - 3y² - 1) + i(6xy + 2y),
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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Transcribed Image Text:7.4. For each of the following functions, determine the set of points at
which it is (i) differentiable and (ii) analytic. Find the derivative where it
exists.
(a). f(z) = (x³ + 3xy² − 3x) +i(y³ + 3x²y - 3y),
(b). f(z) = 6z² - 2z - 4i|z|²,
(c). f(z) = (3x² + 2x − 3y² − 1) +i(6xy + 2y),
Analytic Functions II
2z² +6
z(z² + 4)'
(e). f(z) = ey²-² (cos(2xy) - i sin(2xy)).
(d). f(z) =
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