Could someone advise me how to use Liouville's Theorem to show that there is at least one value z0 in complex plain for which:
|cos (zo/2009)| > 2009
Thank you.
Consider the function . This is an entire function. If on the complex plane then would be a constant function which it is not (by Louiville's theorem). Therefore, there has to exists at least one point so that .