2005 Putnam A3

Let $p(z)$ be a polynomial of degree $n$ all of whose zeros have absolute

value 1 in the complex plane. Put $g(z) = p(z)/z^{n/2}$. Show that all zeros

of $g'(z) = 0$ have absolute value 1.

令 $p(z)$ 为 $n$ 次多项式，其所有零点均具有绝对值

复平面中的值 1。输入 $g(z) = p(z)/z^{n/2}$。表明全为零

$g'(z) = 0$ 的绝对值为 1。