(a) Let $\alpha \in \mathbb { C }$ be an algebraic integer of degree 2 and of modulus 1. Show that $\alpha$ is a root of unity. (b) Show that $\frac { 3 + 4 i } { 5 }$ is an algebraic number of degree 2 and of modulus 1 but is not a root of unity.
(a) Let $\alpha \in \mathbb { C }$ be an algebraic integer of degree 2 and of modulus 1. Show that $\alpha$ is a root of unity.\\
(b) Show that $\frac { 3 + 4 i } { 5 }$ is an algebraic number of degree 2 and of modulus 1 but is not a root of unity.