(Credits: This que is taken from NBHM 2022, which is written in terms of equivalent condition of this using topology and closed set)
I tried $z^{15}-1$ is a trivial polynomial having one of its roots. And suspected that the least degree polynomial divides this.
So I tried to factorize this. $z^{15} -1=(z-1)(1+z+ ...z^{14})$
Then since clearly $z \ne 1 $, I suspected the least degree polynomial divides $(1+z+ ...z^{14})$
Tried to factorize (like grouping 5 terms and taking common term outside) and also(like grouping 3 terms).
But I don't clearly get the way to solve further claiming the root lies in which factor.