1. Yes. |f(z)| = |an z^n +...+ a0 | <= |an||z|^n + ... + |a0|
2. When |z| is big enough this is true. While if z is relatively small consider the example f(z)=1-z. |f(1)|=0<1=|f(0)|
if is a polynomial with a complex number. Then, is it always true that if the domain of is bounded then must be a bounded function?
Also, is it aways true that as we increase we see that increase also? I think this must be the case as polynomials only admit non negative powers.
any help or clarification would be appreciate!