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 = a omega + b omega^(2), z= a omega^(2) + b omega , then the value of x^(3) + y^(3) + z^(3) is equal to (where omega is imaginary cube root of unity)

Evalute: |{:(1,omega^3,omega^2),(omega^3,1,omega),(omega^2,omega,1):}| , where omega is an imaginary cube root 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

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 .

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 .

|{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where omega is an imaginary cube root of 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)