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(c) Show that the only analytic function f: C → C of the form f(x + iy) = u(x) + iv(y) is given by f(z) = Az +a for some À E R and a E C.

(c) Show that the only analytic function f: C → C of the form f(x + iy) = u(x) + iv(y) is given by f(z) = Az +a for some À E R and a 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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(c) Show that the only analytic function f : C → C of the form f(x + iy) = u(x) + iv(y) is given by f(z) = Az + a for some À E R and a € C.
Transcribed Image Text:(c) Show that the only analytic function f : C → C of the form f(x + iy) = u(x) + iv(y) is given by f(z) = Az + a for some À E R and a € C.
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