Let $\alpha, \beta$ be two complex numbers with $\beta \neq 0$, and $f(z)$ a polynomial function on $\mathbb{C}$ such that $f(z) = \alpha$ whenever $z^5 = \beta$. What can you say about the degree of the polynomial $f(z)$?
Let $\alpha, \beta$ be two complex numbers with $\beta \neq 0$, and $f(z)$ a polynomial function on $\mathbb{C}$ such that $f(z) = \alpha$ whenever $z^5 = \beta$. What can you say about the degree of the polynomial $f(z)$?