Suppose $\displaystyle a,b \in \mathbb{R}$ are such that the complex number $\displaystyle a+bi$ is a root of unity and $\displaystyle p(a)=0$ for some monic polynomial $\displaystyle p(x) \in \mathbb{Z}[x].$ Show that $\displaystyle a \in \{-1,0,1 \}.$