Let $\omega \in \mathbb{C}$ be a primitive third root of unity. How many distinct possible images of $\omega$ are there under all the field homomorphisms $\mathbb{Q}(\omega) \longrightarrow \mathbb{C}$.
Let $\omega \in \mathbb{C}$ be a primitive third root of unity. How many distinct possible images of $\omega$ are there under all the field homomorphisms $\mathbb{Q}(\omega) \longrightarrow \mathbb{C}$.