All Complex Analysis Resources
Example Questions
Example Question #1 : Analytic And Harmonic Functions
Find a Harmonic Conjugate of
Possible Answers:
Correct answer:
Explanation:
is said to be a harmonic conjugate of
if their are both harmonic in their domain and their first order partial derivatives satisfy the Cauchy-Riemann Equations. Computing the partial derivatives
where is any arbitrary constant.
Example Question #1 : Analytic And Harmonic Functions
Given , where does
exist?
Possible Answers:
Nowhere
The Entire Complex Plane
Correct answer:
Nowhere
Explanation:
Rewriting in real and complex components, we have that
So this implies that
where
Therefore, checking the Cauchy-Riemann Equations, we have that
So the Cauchy-Riemann equations are never satisfied on the entire complex plane, so is differentiable nowhere.
Brian
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Cooper Union for the Advancement of Science and Art, Bachelor of Science, Electrical Engineering.
Ram
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Andhra Loyola College, Bachelor of Chemistry, Chemistry. West Virginia University, Doctor of Philosophy, Organic Chemistry.
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