Normalising vectors - in the complex case

hi guys,

Im having difficulty interpreting the norm of vectors with complex entries.( i understand in the real case that to nomalise a vector you sum up the squares of the entries, take the square root of the total and that gives the norm, and the you multiply the original vector by 1/norm to normalise it) but with in terms of dealing with complex entries i don't seem to be getting the right answers, please could you explain why....(please note the vectors are in transposed form)

1/2(1−*i*, 2, 1+*i) *

*when normalised gives *

(root2)/4 (1−*i*, 2 ,1+*i) (implying the norm is root 2)*

*or if its easier please explain why the normalised version of this vector :*

*(**i*,1−*i*,−1) is

*1/2(**i*,1−*i*,−1)

thanks so much in advance.