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. 

There is the following general theorem:

Let $A$ be a central simple $k$-algebra and $B$ a simple $k$-algebra with center $T$. Then $A \otimes_k B$ is a simple $k$-algebra with center $1 \otimes_k T$.

You can find the proof in any introductory book of non-commutative ring theory. It is Theorem 3.60 in "Methods of Representation Theory" by Curtis and Reiner.
