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. (a) Show that f(x). 28²

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. (a) Show that f(x). 28²

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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Question

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.
(a) Show that f(z) = z — iz².

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