## Ring isomorphism

Hello,

the ring of gaussian integers $\mathbb Z[i]$ is isomorphic to the ring $\mathbb Z[x]/(x^2+1)$.

Using this fact, why are the rings $\mathbb Z[i]/p \mathbb Z[i]$ and $\mathbb F_p[x]/(x^2+1)\mathbb F_p[x]$ isomorphic?