OK, so when I normalize the vector do i take the result ,and then find the complement of that. For a complement to be perpendicular do we take an arbitrary vector (a,b,c) and find the inner product of our new found vector with the arbitrary vector and it has to equal zero?

W basis = ((radical 2)/2) (i,0,1)

So W complement = <W basis, (a,b,c)> =0 so (a,b,c) = (1, a, i) where a is any scalar in C?