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3. After showing that the function u(x, y) 2³ + a2 – 3xy? + x – y? + 1 is harmonic, find a function v such that f(x+iy) = u(x, y) +iv(x, y) is analytic. Write the formula of f in terms of z = x + iy.

3. After showing that the function u(x, y) 2³ + a2 – 3xy? + x – y? + 1 is harmonic, find a function v such that f(x+iy) = u(x, y) +iv(x, y) is analytic. Write the formula of f in terms of z = x + iy.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Complex Numbers
Section4.2: Complex Solutions Of Equations
Problem 7ECP: Find the cubic polynomial function f with real coefficients that has 1 and 2+i as zeros, and f2=2.
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After showing that the function u(x, y) 23 + x? – 3xy? + x – y² + 1 is harmonic, find a function v such that f(x+iy) = u(x, y) +iv(x, y) is analytic. Write the formula of f in terms of z = x + iy. 3.
Transcribed Image Text:After showing that the function u(x, y) 23 + x? – 3xy? + x – y² + 1 is harmonic, find a function v such that f(x+iy) = u(x, y) +iv(x, y) is analytic. Write the formula of f in terms of z = x + iy. 3.
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