# Analytic Functions : Constancy

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7. Let a function f (z) be a analytic in a domain D. Prove that f (z) must be constant throughout D if

(a) f (z) is real-valued for all z in D

(b) | f (z) | is constant throughout D.

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7. Let a function f (z) be a analytic in a domain D. Prove that f (z) must be constant throughout D if

(a) f (z) is real-valued for all z in D

Denote where u(x,y) and v(x,y) are real ...

#### Solution Summary

The constancy of analytic functions is investigated. The solution is detailed and well presented.

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