If `x=omega-omega^2-2` then , the value of `x^4+3x^3+2x^2-11x-6` is (where `omega ` is a imaginary cube root of unity)

If x=a+b, y=aomega+bomega^2 and z=aomega^2+bomega where omega is an imaginary cube root of unity, prove that x^2+y^2+z^2=6ab .

Evaluate: | (1, 1, 1), (1, omega^2, omega), (1, omega, omega^2)| (where omega is an imaginary cube root unity).

The polynomial x^(6)+4x^(5)+3x^(4)+2x^(3)+x+1 is divisible by: (where omega is one of the imaginary cube roots of unity)

The value of the expression 1.(2-omega).(2-omega^2)+2.(3-omega)(3-omega^2)+.+(n-1)(n-omega)(n-omega^2), where omega is an imaginary cube root of unity, is………

The value of w^2+w^5+w^8+3w+3 is, (where w is a non real cube root of unity)