`|(1,omega^4,omega^2),(omega^4,1,omega^3),(omega^2,omega,1)| = ?`

If omega is cube root of unit, then find the value of determinant |(1,omega^3,omega^2), (omega^3,1,omega), (omega^2,omega,1)|.

{[(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))]

If omega is cube roots of unity, prove that {[(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)]=[(0),(0),(0)]

The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,omega^(4)),(omega^(5),omega^(4),1)| , where omega is an imaginary cube root of unity, is

Suppose omega!=1 is a sube root of unity, and Delta=|(1,omega^(2),1-omega^(4)),(omega,1,1+omega^(5)),(1,omega,omega^(2))| then |Re(Delta)|= _____________

If omega is an imaginary cube root of unity, then the value of |(1,omega^(2),1-omega^(4)),(omega,1,1+omega^(5)),(1,omega,omega^(2))| is