Let be a polynomial of degree greater than 1, with all of it's zeroes inside the circle . show that .
My idea for a proof:
Since every polynomial over can be writen as , where are all the zeroes of (not necessarily unique). Than we can write .
Now we can say that for every we can find a circle such that
and therfore is analytic in so we get , but since we have and that shows what we needed to show.
I would appreciate some thoughts on this proof as I am not 100% sure it is valid.