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1. Let f(x+iy) = u(x, y) + iv(x, y), where u : R² → R and v : R² → R are defined by u(x, y) = x + 2xy, v(x, y) = y² – x² — y. This defines a corresponding complex function f: C → C. (b) Use the definition of the derivative to show that f is not (complex) differentiable at any point zo E C.

1. Let f(x+iy) = u(x, y) + iv(x, y), where u : R² → R and v : R² → R are defined by u(x, y) = x + 2xy, v(x, y) = y² – x² — y. This defines a corresponding complex function f: C → C. (b) Use the definition of the derivative to show that f is not (complex) differentiable at any point zo E C.

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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1. Let f(x+iy) = u(x, y) + iv(x, y), where u : R² → R and v : R² → R are defined by u(x, y) = x + 2xy, v(x, y) = y² — x² — y. This defines a corresponding complex function ƒ : C → C. (b) Use the definition of the derivative to show that f is not (complex) differentiable at any point zo E C.
Transcribed Image Text:1. Let f(x+iy) = u(x, y) + iv(x, y), where u : R² → R and v : R² → R are defined by u(x, y) = x + 2xy, v(x, y) = y² — x² — y. This defines a corresponding complex function ƒ : C → C. (b) Use the definition of the derivative to show that f is not (complex) differentiable at any point zo E C.
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