Prove that
`(2+omega+omega^2)^3+(1+omega-omega^2)^8-(1-3omega+omega^2)^4 = 1`

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

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

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

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

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

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

If omega is a complex cube root of unity,show 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)]=[000]

(2 + omega + omega ^ (2)) ^ (3) + (1 + omega-omega ^ (2)) ^ (3) = (1-3 omega + omega ^ (2)) ^ (4) = 1