# Let G be a region and suppose that f:G->C (C here is complex plane)is analytic and a in G such that |f(a)|=<|f(z)| for all z in G. Show that either f(a) = 0 or f is constant.

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Let G be a region and suppose that f:G->C (C here is complex plane)is analytic and a in G such that |f(a)|=<|f(z)| for all z in G.

Show that either f(a) = 0 or f is constant.

https://brainmass.com/math/complex-analysis/56582

#### Solution Preview

Proof:

If f(a)=0, we are done.

If f(a)<>0 ("<>" means not equal to), then we set g(z)=1/f(z). Because ...

#### Solution Summary

Analytic functions and complex integration are investigated.

$2.49