All Complex Analysis Resources
Example Questions
Example Question #23 : Complex Analysis
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 #24 : Complex Analysis
Given , where does exist?
Possible Answers:
The Entire Complex Plane
Nowhere
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.
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