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………

Sum the series : 1(2-omega)(2-omega^(2))+2(3-omega)(3-omega^(2))......(n-1)(n-omega)(n-omega^(2)) where omega and omega^(2) are non-real cube roots of unity.

|{:(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega):}|=0 where omega is an 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 .

Evaluate abs((1,omega,omega^2),(omega^2,1,omega),(omega^2,omega,1)) were omega is an imaginary cube root of unity.

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

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

The value of the expression , (2-w)(2-w^2)+2.(3-w)(3-w^2)+....... ...... +(n-1).(n-w)(n-w^2) , where w 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

If omega is a complex cube root of unity,then the value of the expression 1(2-omega)(2-omega^(2))+2(3-omega)(3-omega^(2))+...+(n-1)(n-omega)(n-omega^(2))(n-omega^(2))(n>=2) is equal to (A) (n^(2)(n+1)^(2))/(4)-n( B) (n^(2)(n+1)^(2))/(4)+n( C) (n^(2)(n+1))/(4)-n(D)(n(n+1)^(2))/(4)-n