Complex Analysis : Applications of Harmonic Functions

Study concepts, example questions & explanations for Complex Analysis

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Example Questions

Example Question #1 :Applications Of Harmonic Functions

Ifandare both analytic through a domain, which of the following is true?

Possible Answers:

is nowhere differentiable

is nowhere analytic

None of the other answers

must be constant throughout

Correct answer:

must be constant throughout

Explanation:

Sinceis analytic, the Cauchy-Riemann Equations give us

Sinceis analytic, the Cauchy-Riemann Equations give us.

Putting these two results together gives us

which implies thatis constant. Similar reasoning gives is thatis constant. This implies thatmust be constant throughout.

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