As an exercise convert the linearly independent set \begin{equation*} S=\set{ \colvector{1+i\\1\\1-i\\i},\, \colvector{i\\1+i\\-1\\-i},\, \colvector{i\\-i\\ -1+i\\1},\, \colvector{-1-i\\i\\1\\-1} } \end{equation*} to an orthogonal set via the Gram-Schmidt Process (Theorem GSP) and then scale the vectors to norm 1 to create an orthonormal set. You should get the same set you would if you scaled the orthogonal set of Example AOS to become an orthonormal set.