Is $e^{i\theta}$ where $\theta = \frac{2\pi}{n}, n \in \mathbb{N}$ algebraic over $\mathbb{Q}$?

Question

I am not sure how to come up with a $p(x) \in \mathbb{Q}[x]$ such that $e^{i\theta}$ is a solution so I feel like it is not algebraic over $\mathbb{Q}$.

Answer 1

The complex number $e^{2\pi i/n}$ is one of the roots of $x^n-1$. It is called an $n$th root of unity.