8. If `w^3=1` and `w !=0` then find the value of `(1+w) (1+w^2)(1+w^3)(1+w^4)`

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

(1)/(a + omega) + (1)/(b+omega) +(1)/(c + omega) + (1)/(d + omega) =(1)/(omega) where, a,b,c,d, in R and omega is a complex cube root of unity then find the value of sum (1)/(a^(2)-a+1)

if omegaa n domega^2 are the nonreal cube roots of unity and [1//(a+omega)]+[1//(b+omega)]+[1//(c+omega)]=2omega^2 and [1//(a+omega)^2]+[1//(b+omega)^2]+[1//(c+omega)^2]=2omega^ , then find the value of [1//(a+1)]+[1//(b+1)]+[1//(c+1)]dot

if omegaa n domega^2 are the nonreal cube roots of unity and [1//(a+omega)]+[1//(b+omega)]+[1//(c+omega)]=2omega^2 and [1//(a+omega)^2]+[1//(b+omega)^2]+[1//(c+omega)^2]=2omega^ , then find the value of [1//(a+1)]+[1//(b+1)]+[1//(c+1)]dot

If 1,x_(1),x_(2),x_(3) are the roots of x^(4)-1=0andomega is a complex cube root of unity, find the value of ((omega^(2)-x_(1))(omega^(2)-x_(2))(omega^(2)-x_(3)))/((omega-x_(1))(omega-x_(2))(omega-x_(3)))

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]|