Simplify `omega(1+omega)-omega^2`

omega(1+omega-omega^(2))=-2

Prove that (1-omega-omega^(2))(1-omega+omega^(2))(1+omega-omega^(2))=8

det [[1, omega, omega^(2) omega, omega^(2), 1omega^(2), 1, omega]]

det [[1, omega, omega^(2) omega, omega^(2), 1omega^(2), 1, omega]] =

If 1, omega, omega^2 be three roots of 1, show that: (1-omega+omega^2)^2+(1+omega-omega^2)^2=-4

(1-omega+omega^(2))(1+omega-omega^(2))=4

Let omega=-(1)/(2)+i(sqrt(3))/(2), then value of the determinant [[1,1,11,-1,-omega^(2)omega^(2),omega^(2),omega]] is (a) 3 omega(b)3 omega(omega-1)3 omega^(2)(d)3 omega(1-omega)