Show that `\begin{vmatrix}1& \omega & (\omega)^2\\ \omega &1 & (\omega)^2\\ \omega & (\omega)^2 & 1 \end{vmatrix} =0`

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

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

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

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

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]

Show that (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))...... to 2 n factors =2^(2n)

(1)/(2+omega)+(1)/(1+2 omega)=(1)/(1+omega)

(1)/(2+omega)+(1)/(1+2 omega)=(1)/(1+omega)