Q: For fixed $\displaystyle a\in{\mathbb{C}}$ find the value of $\displaystyle |z^{n}-a|$ that is maximized when $\displaystyle |z|<1$.

A: Well, I would think I need to find the the roots to the equation $\displaystyle z^{n}=a$ firs. After that I am not sure. Since this is a max question, I feel that I need to take the derivative at some point with respect to z.

Any help would be appreciated.

Thanks