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!=1 is a cube root of unity and Delta=|(x+omega^(2),omega,1),(omega,omega^(2),1+x),(1,x+omega,omega^(2))|=0 then value of x is

If omega ne 1 is a cube root of unity, then 1, omega, omega^(2)

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

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

If w is a complex cube root of unity, then the value of the determinant Delta = [(1,w,w^(2)),(w,w^(2),1),(w^(2),1,w)] , is

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 complex cube root of unity, then (x+1)(x+omega)(x-omega-1)