$p$ odd prime and $n$ integer. Prove that $x^n - p$ is irreducible over $\mathbb{Z}[i]$

Question

By Eisenstein's criterion I know that the polynomial is irreducible in $\mathbb{Z}[X]$, since $p$ divides $p$ and $p^2$ does not divide $p$. But I do not know how to extend to $\mathbb{Z}[i]$.