1. Verify directly that the real and imaginary parts of the following analytic functions satisfy Laplace's equation: (a) f(2)=z²+2z+1 (b) g(z) = ¹ (c) h(z) = e²
1. Verify directly that the real and imaginary parts of the following analytic functions satisfy Laplace's equation: (a) f(2)=z²+2z+1 (b) g(z) = ¹ (c) h(z) = e²
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Question
Verify directly that the real and imaginary parts of the following analytic functions satisfy
Laplace’s equation:
(a) f(z) = z
2 + 2z + 1
(b) g(z) = 1
z
(c) h(z) = e
z
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