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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
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.
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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