|[1,omega,omega^(2)],[omega,omega^(2),1],[omega^(2),1,omega]|=0

If omega is a complex cube root of unity.Show that Det[[1,omega,omega^(2)omega,omega^(2),1omega^(2),1,omega]]=0

If omega is complex cube root of 1 then S.T [(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)]=0

If omega is a complex cube root of unity then a root of the equation |[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+omega]|=0 is

Let omega be the complex number cos (2 pi)/(3)+i sin (2 pi)/(3) . Then the number of distinct complex number z satisfying [[z+1,omega,omega^(2)],[omega,z+omega^2,1],[omega^(2),1,z+omega]] = 0 is equal to

Evaluate the following determinants. [[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]]

If omega=-(1)/(2)+i (sqrt(3))/(2) , the value of [[1, omega, omega^(2) ],[ omega, omega^(2), 1],[ omega^(2),1, omega]] is

Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+omega]] =0

Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number of distinct complex numbers z satisfying abs[[z+1,omega,omega^2],[omega,(z+omega^2),1],[omega^2,1 ,z+omega]]=0 is equals to

{[(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)] + [(omega,omega^(2),1),(omega^(2),1,omega),(omega,omega^(2),1)]} [(1),(omega),(omega^(2))]

find determinant of |(1, omega, omega^(2)),(omega, omega^(2),1),(omega^(2),1,omega)|=