eigenvalues of (real?) orthogonal matrices have magnitude 1

Hi all, just wanted to make sure I have this right -

My lecture notes say that the eigenvalues of orthogonal matrices have magnitude 1. When I looked through the proof it seemed to me like the statement should have said *real* orthogonal matrices.

So I played around a little bit and I think I came up with a counterexample to show the eigenvalues of any orthogonal matrix don't have magnitude 1:

(LaTeX isn't co-operating, sorry)

Q = [2i, sqrt{5} ; sqrt{5}, -2i]

is orthogonal but has eigenvalues 2i & -1/(2i), which don't have magnitude 1...

All good? Anything I missed?

Thanks a lot