Let ƒ: C → C be the function defined by ƒ(z) = izz. (c) Write in the form f(x + iy) = u(x, y) + iv(x, y) where u, v : R² → R, and verify that the Cauchy-Riemann equations are satisfied if and only if x = y = 0.
Let ƒ: C → C be the function defined by ƒ(z) = izz. (c) Write in the form f(x + iy) = u(x, y) + iv(x, y) where u, v : R² → R, and verify that the Cauchy-Riemann equations are satisfied if and only if x = y = 0.
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:Let f: C→C be the function defined by ƒ(z) = izz.
(c) Write f in the form
f(x + iy) u{(2,y)+iz(x,y)
where u, v : R² → R, and verify that the Cauchy-Riemann equations are satisfied
if and only if x = y = 0.
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