Find the sum `1xx(2-omega)xx(2-omega^(2))+2xx(-3-omega)xx(3-omega^(2))+….+(n-1)xx(n-omega)xx(n-omega^(2))`, 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………

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

The value of the expression 2(1+(1)/(omega))(1+(1)/(omega^(2)))+3(2+(1)/(omega))(2+(1)/(omega^(2)))+4(3+(1)/(omega^()))(3+(1)/(omega^(2)))+.......+(n+1)(n+(1)/(omega^()))(n+(1)/(omega^(2))) where omega is an imaginary cube roots of unity, is:

The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,omega^(4)),(omega^(5),omega^(4),1)| , where omega is an imaginary cube root of unity, is

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=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)

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega, omega)| where omega is cube root of unity.

Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

Prove the following (1- omega + omega^(2)) (1- omega^(2) + omega^(4)) (1- omega^(4) + omega^(8)) …. to 2n factors = 2^(2n) where , ω is the cube root of unity.

If A =({:( 1,1,1),( 1,omega ^(2) , omega ),( 1 ,omega , omega ^(2)) :}) where omega is a complex cube root of unity then adj -A equals