# Complex analysis for Unit Circle

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Let f be analytic inside and on the unit circle. Suppose that 0<|f(z)|<1 if |z| = 1.

Show that f has exactly one fixed point inside the unit circle. ( note : a fixed point is a point Zo such that f(Zo) = Zo).

https://brainmass.com/math/complex-analysis/complex-analysis-unit-circle-185606

#### Solution Preview

For |z| = 1 we have

|-z| = 1 > |f(z)|

So by Rouche's ...

#### Solution Summary

The expert examines a complex analysis for Unit Circles.

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