$\mathbb{F}_p({\rm i}) = \mathbb{F}_{p^2}$ iff $p=3\mod 4$

Question

I know the fact that \begin{equation*} \mathbb{F}_{p^2} = \mathbb{F}_p({\rm i}) \simeq \mathbb{F}_p[x]/(x^2+1) \end{equation*} for a unit ${\rm i}$, i.e. ${\rm i}^2=-1$, iff $p=3\ {\rm mod}\ 4$ for a prime p, but I can't show or find its proof.

Can anyone show this or tell me a good URL ?

Thank you in advance.