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 1,alpha_1,alpha_2,alpha_3,alpha_4 be the roots x^5-1=0 , then value of [omega-alpha_1]/[omega^2-alpha_1].[omega-alpha_2]/[omega^2-alpha_2].[omega-alpha_3]/[omega^2-alpha_3].[omega-alpha_4]/[omega^2-alpha_4] is (where omega is 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 .

If omega is a cube root of unity, then omega^(3) = ……

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 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

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. (a) x+omega (b) x+omega^2 (c) (x+omega)(x+omega^2) (d) (x-omega)(x-omega^2)

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

If omega is a cube root of unity, then 1+ omega^(2)= …..

The common roots of the equation x^(3) + 2x^(2) + 2x + 1 = 0 and 1+ x^(2008)+ x^(2003) = 0 are (where omega is a complex cube root of unity)

If f(x)=a+b x+c x^2AAa ,b ,c in R and a ,b ,c are distinct, then value of |a b c b c a c a b| is (where omega&omega^2 are complex cube roots of unity) f(1)f(omega)f(omega^2) (b) -f(omega)f(omega^2) -f(1)f(omega)f(omega^2) (d) f(omega)f(omega^2)