If `w` is cube roots of unity, then find the value of`w^2+w^3+w^4`

If omega is a cube root of unity, then find the value of the following: (1+omega-omega^2)(1-omega+omega^2)

If omega is a cube root of unity, then find the value of the following: (1-omega)(1-omega^2)(1-omega^4)(1-omega^8)

If omega is a complex cube roots of unity, then find the value of the (1+ omega)(1+ omega^(2))(1+ omega^(4)) (1+ omega^(8)) … to 2n factors.

If omega!=1 is a cube root of unity, then find the value of |[1+2omega^100+omega^200,omega^2,1],[1,1+omega^100+2omega^200,omega],[omega,omega^2,2+omega^100+omega^200]|

If omega is a cube root of unity then find the value of sin((omega^(10)+omega^(23))pi -pi/4)

If omega is a cube root of unity then find the value of sin((omega^(10)+omega^(23))pi-pi/4)

If w is an imaginary cube root of unity, find the value of |[1,w, w^2],[ w ,w^2 ,1],[w^2 ,1,w]| .

If omega is an imaginary cube root of unity, then find the value of (1+omega)(1+omega^2)(1+omega^3)(1+omega^4)(1+omega^5)........(1+omega^(3n))=

If omega is the complex cube root of unity, then the value of omega+omega ^(1/2+3/8+9/32+27/128+………..) ,

If omega is an imaginary cube root of unity, then the value of the determinant |(1+omega,omega^2,-omega),(1+omega^2,omega,-omega^2),(omega+omega^2,omega,-omega^2)|