## Orthanormal set in C^3

hi

Let w = exp{2pi(i)/3}. Show that v_1, v_2, v_3 form an orthanormal set in C^3 where

v_1 = (1/sqrt(3))*[1 1 1]^T

v_2 = (1/sqrt(3))*[1 w w^2]^T

v_3 = (1/sqrt(3))*[1 w^2 w^4]^T

thoughts...

(1) The question has no mention that v_1, v_2, and v_3 form a basis, so i'm assuming they do?

(2) we use the Gram Schmidt theorem for this problem??

(3) I know that [exp{2pi(i)/3}]^2 = -1/2 - (sqrt(3)/2)i

and,

[exp{2pi(i)/3}]^4 = -1/2 + (sqrt(3)/2)i

I'm told there is a big short-cut with this ques...any hints or suggestions recieved with thanks.

best