The splittness symplectic group over a totally real number field or totally imaginary number field

Question

Let $F$ be a number field either totally real or totally imaginary.

$H$ be a hyperbolic plane over $F$ and $W=H^n$ be a $n$-fold direct sum of $H$.

Consider the isometric group $Sp(W)$ on $W$.

I am wondering whether $Sp(W)$ is split over $F$ regardless of $F$ is totally real or totally imaginary.