If $\alpha$ is an algebraic number with minimal polynomial $\Pi _ { \alpha }$, the complex roots of $\Pi _ { \alpha }$ different from $\alpha$ are called the conjugates of $\alpha$. We denote by $C ( \alpha )$ the set of conjugates of $\alpha$.
Let $x$ be an algebraic number of modulus 1 and such that $x \notin \{ - 1,1 \}$. Show that $\frac { 1 } { x }$ is a conjugate of $x$. Deduce that $\Pi _ { x }$ is reciprocal.