`(omega^2 + omega^3 + omega^4)`

If omega is cube root of unit, then find the value of determinant |(1,omega^3,omega^2), (omega^3,1,omega), (omega^2,omega,1)|.

If omega is the complex cube root of unity,then prove that det[[1,1,11,-1-omega^(2),omega^(2)1,omega^(2),omega^(4)]]=+-3sqrt(3)i

Find the value of |{:(" "1+i," "i omega," "i omega^(2)),(" "i omega," "i omega^(2)+1," "i omega^(3)),(i omega^(2), i omega^(3), " "i omega^(4)+1):}| , where omega is a non real cube root of unity and i = sqrt(-1) .

Solve: /_\ = |[omega^(3),omega^(4),omega^(5)],[omega^(6),omega^(8),omega^(2)],[omega^(7),omega^(9),omega]|