Computing the center of a ring if i have the following ring  $R = \mathbb{H} \otimes _\mathbb{R} M_2(\mathbb{C}) $
then how would i find the center $Z(R)$? 
Also is this ring simple, i am sure it is but am struggling to show that is actually is
Any help would be really useful and greatly appreciated
thank you. 

Clearly $Z(\Bbb H)\otimes_\Bbb R Z(M_2(\Bbb C))$ is in the center of the tensor product. Now $Z(\Bbb H)=\Bbb R$ and $Z(M_2(\Bbb C))\cong \Bbb C$, so we're looking at $\Bbb R\otimes_\Bbb R \Bbb C\cong \Bbb C$ as $\Bbb R$ algebras. We're looking for a copy of $\Bbb C$ inside this ring.
Clearly $Z(\Bbb H)\otimes_\Bbb R Z(M_2(\Bbb C))=\{1\otimes \begin{bmatrix}c&0\\0&c\end{bmatrix}\mid c\in \Bbb C\}$ is the copy we're looking for.
