If $X=Gr_{n,k}(\mathbb{R})$ is a real Grassmann variety (of $k$-planes in $n$-dimensional space), then what is $X(\mathbb{C})$, the set of complex points of $X$? In particular, can it be identified as a complex Grassmann variety?
If this is trivial and/or immediate from definitions, then a good reference for this material would be appreciated.