Prove that
`(1+2omega+3omega^2)/(2+3omega+omega^2) + (2+3omega+omega^2)/(3+omega+2omega^2) = 2omega`

If omega is a non-real cube root of unity, then (1+2omega+3omega^2)/(2+3omega+omega^2)+(2+3omega+omega^2)/(3+omega+2omega^2) is equal to

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

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]

Prove that (p+q omega+r omega^(2))/(r+p omega+q omega^(2))=omega^(2)

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

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

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)]

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

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