Find the value of `(1+w-w^2)^5+(1-w+w^2)^5`

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 1,omega,omega^(2),...omega^(n-1) are n, nth roots of unity, find the value of (9-omega)(9-omega^(2))...(9-omega^(n-1)).

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 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 w=cos""(pi)/(n)+isin""(pi)/(n) then value of 1+w+w^(2)+.......+w^(n-1) is :

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)

(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: [(xy,5x) , (z+6,y^2+1)]=[(8,w),(0,6)], then find the values of x , y , z and w

If 1 , omega, omega^(2) are cube roots of unity then the value of (5+2omega +5omega^(2))^(3) is