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## Homework Statement

Let [tex]f(z)=\sum_{n=0}^{\infty} a_n z^n [/tex] be analytic at {z: |z|<R} and satisfies:

[tex] |f(z)| \leq M [/tex] for every |z|<R.

Let's define: d=the distance between the origin and the closest zero of f(z).

Prove: [tex] d \geq \frac{R|a_0|}{M+|a_0|} [/tex].

Hope you'll be able to help me

Thanks !

## Homework Equations

## The Attempt at a Solution

I've tried using Cauchy's Inequality... But it doesn't give anything new for [tex] a_0 [/tex].

I've also tried isolating [tex] a_0 [/tex] from this inequality, but it gives me nothing...

Hope someone will be able to help me

Thanks in advance