## Complex Analysis-Taylor Series

Let $f(z)=\sum_{n=0}^{\infty} a_n z^n$ be analytic at {z: |z|<R} and satisfies:
$|f(z)| \leq M$ for every |z|<R.
Let's define: d=the distance between the origin and the closest zero of f(z).
Prove: $d \geq \frac{R|a_0|}{M+|a_0|}$.
Hope you'll be able to help me

Thanks !