Prove that an algebraic integer is a unit in Z(a)

1. Mar 7, 2013

lahuxixi

I'm completely stuck here, can anyone help me?

2. Mar 7, 2013

Dick

You shouldn't be completely stuck. One direction at least is easy. $\alpha^n+a_{n-1}\alpha^{n-1}+...+a_1 \alpha=-a_0$. Can you show that if $a_0=\pm 1$ then $\alpha$ is a unit?