Hi,

if $\displaystyle f(z)$ is a polynomial with $\displaystyle z$ a complex number. Then, is it always true that if the domain of $\displaystyle f$ is bounded then $\displaystyle f$ must be a bounded function?

Also, is it aways true that as we increase $\displaystyle |z|$ we see that $\displaystyle |f(z)|$ increase also? I think this must be the case as polynomials only admit non negative powers.

any help or clarification would be appreciate!

Thanks