Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+...+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$
42988
Complex polynomial and the unit circle
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
118916
How do I prove that a polynomial F[x] of degree n has at most n roots
44802
The $n$ complex $n$th roots of a complex number $z$
89509
Suppose $z \neq -1$ is a complex number of norm 1. Prove that $(\frac{1+z}{|1+z|})^2 =z $
158524
Complex numbers $z$ such that $|z|= 1$
68776
Solve in $C$ : $P(z)=z^4+2z^3+5z^2+4z+1=0$ where $P(i-\frac{1}{2}+i\frac{\sqrt 3}{2})=0$
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
54059
Showing that $\frac{z^n}{1+z^{2n}}$ is real for $|z|=1$.
131869
How to find all polynomials P(x) such that $P(x^2-2)=P(x)^2 -2$?
149544
maximum of monic polynomial on unit circle is 1 implies $p(z)=z^n$
82204
Prove $ \lim_{n\to\infty}\sqrt[n]{p(n)}=1 $ for polynomial
118085
complex polynomial satisfying inequality
73419
For $f$ entire and $\{f(kz) : k \in \mathbb{C}\}$ a normal family, prove that $f$ is a polynomial.
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
27062
Given complex $|z_{1}| = 2\;\;,|z_{2}| = 3\;\;, |z_{3}| = 4\;\;$ : when and what is $\max$ of $|z_{1}-z_{2}|^2+|z_{2}-z_{3}|^2+|z_{3}-z_{1}|^2$
121404
How to factor polynomials in $\mathbb{Z}_n$?