Consider a complex function f(z) = u(x, y) +iv(x, y), z = x+iy, with real and imaginary parts give by u(x, y) = 3x²y², v(x, y) = -6x²y². Determine where this function is differentiable with respect to z. Determine where this function is analytic.
Consider a complex function f(z) = u(x, y) +iv(x, y), z = x+iy, with real and imaginary parts give by u(x, y) = 3x²y², v(x, y) = -6x²y². Determine where this function is differentiable with respect to z. Determine where this function is analytic.
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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![Consider a complex function ƒ(z) = u(x, y) + iv(x, y), z = x+iy, with real and imaginary parts given
by
u(x, y) = 3x²y²,
v(x, y) = -6x²y².
Determine where this function is differentiable with respect to z.
Determine where this function is analytic.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F335d6cef-e110-4df1-b3c9-cf74ce65a19c%2Fca46706b-2b02-4934-a2af-034da10c3a16%2F4m3m56a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a complex function ƒ(z) = u(x, y) + iv(x, y), z = x+iy, with real and imaginary parts given
by
u(x, y) = 3x²y²,
v(x, y) = -6x²y².
Determine where this function is differentiable with respect to z.
Determine where this function is analytic.
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