If `w` is cube roots of unity then find `|[x+1, w, w^2], [w,x+w^2,1],[w^2,1,x+w]|`

If w is a complex cube root of unity. Show that |[1,w, w^2],[w, w^2, 1],[w^2, 1,w]|=0 .

If w is an imaginary cube root of unity, find the value of |[1,w, w^2],[ w ,w^2 ,1],[w^2 ,1,w]| .

If omega is a cube root of unity, then 1+omega = …..

If omega is a cube root of unity, then 1+ omega^(2)= …..

If omega is a cube root of unity, then omega^(3) = ……

If w ne 1 is a cube root of unity and Delta=|{:(x+w^(2),w,1),(w,w^(2),1+x),(1,x+w,w^(2)):}|=0 , then value of x is

If omega is a cube root of unity, then omega + omega^(2)= …..

If omega is a cube root of unity , then |(x+1 , omega , omega^2),(omega , x+omega^2, 1),(omega^2 , 1, x+omega)| =

If omega is the complex cube root of unity then |[1,1+i+omega^2,omega^2],[1-i,-1,omega^2-1],[-i,-i+omega-1,-1]|=

If w is a complex cube root of unity then show that ( 2 − w ) ( 2 − w^2 ) ( 2 − w^10 ) ( 2 − w^11 ) = 49 ?