Pls help
hinhungoc
I don't think your equation A.B= x1x2* - x2*x1 reflects your problem:
A=[x1, -x2*]
B=[x2, x1*]
Wouldn't it be A.B= x1x2 - x2*x1*??
If not, do you have a mistake with your vectors A or B?
Added after 7 minutes:
honhungoc (sorry about the misspelling)
If your vectors are (rather):
A=[x1,-x2*] and
B=[x2*,x1], then the dot becomes x1x2* - x2*x1 as you indicated in your post.
If so, this does have to be zero, because multiplication of complex numbers is commutative.
(i.e. x1x2* = x2*x1, so x1x2* - x2*x1 = x1x2* - x1x2* = 0)