I have problem with these two exercise:

1. Assume, that $\displaystyle \epsilon \in C$ is a nth root of unity. Show: if $\displaystyle \epsilon \neq 1$, then $\displaystyle \epsilon$ is the root of the syclotomic polynomial $\displaystyle \Phi_n = 1 + X + X^2 + \dots + X^{n-1} \in \mathbb{C}[X]$.

($\displaystyle \epsilon = e^{2\pi i / n}$)

2. Show: if $\displaystyle k \in \mathbb{C}$, then $\displaystyle X^n - k^n = (X-k)(X-\epsilon k) \cdots (X-\epsilon^{n-1}k)$, where $\displaystyle \epsilon = e^{2\pi i / n}$.

I have no idea how to begin with these, so any help would be nice.