If `omega` is a complex cube root of unity, show that `([1omegaomega^2omegaomega^2 1omega^2 1omega]+[omegaomega^2 1omega^2 1omegaomegaomega^2 1])[1omegaomega^2]=[0 0 0]`

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]

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]]=[[0, 0 ,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 a complex cube root of unity, show that (1+omega)^3 - (1+omega^2)^3 =0

If omega is a complex cube root of unity, then (1-omega+(omega)^2)^3 =

If omega is a cube root of unity, prove that (1+omega-omega^2)^3-(1-omega+omega^2)^3=0

If omega be an imaginary cube root of unity, show that (1+omega-omega^2)(1-omega+omega^2)=4

If omega be an imaginary cube root of unity, show that (1+omega-omega^2)(1-omega+omega^2)=4

If omega is a complex cube root of unity, then (1+omega-(omega)^2)^3 - (1-omega+(omega)^2)^3 =

If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)=