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Example Questions
Example Question #1 : Applications Of Harmonic Functions
If and are both analytic through a domain , which of the following is true?
Possible Answers:
is nowhere differentiable
must be constant throughout
None of the other answers
is nowhere analytic
Correct answer:
must be constant throughout
Explanation:
Since is analytic, the Cauchy-Riemann Equations give us
Since is analytic, the Cauchy-Riemann Equations give us .
Putting these two results together gives us
which implies that is constant. Similar reasoning gives is that is constant. This implies that must be constant throughout .
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