From Harvard qualification exam, 1990. Let $f$ be a holomorphic function on a domain contained the closed disc $|z|\le 3$ such that $f(\pm 1)=f(\pm i)=0$ Show that $|f(0) |\le \frac{1}{80}\max |f(z)|_{|z|=3}$
I am confused with this question because I do not know how to use the condition $|z|\le 3$ at all. I also do not know how this related to the four zeros (looks arbitrarily to me). This question feels really standard so I venture to ask in here.