(1) Verify that the real-valued function u(x, y) = xª – 6æ?y? + y* + 4x – 6y + 2 - defined on the complex plane is harmonic, and determine all real-valued functions v such that f = u + iv is analytic on C.

(1) Verify that the real-valued function u(x, y) = xª – 6æ?y? + y* + 4x – 6y + 2 - defined on the complex plane is harmonic, and determine all real-valued functions v such that f = u + iv is analytic on C.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 52E

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Question

(1) Verify that the real-valued function
u(x, y) = xª – 6æ?y? + y* + 4x – 6y + 2
-
defined on the complex plane is harmonic, and determine all real-valued functions
v such that f = u + iv is analytic on C.

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