If `alpha_1,alpha_2,alpha_3,alpha_4` be the roots of `x^5-1`=0 then prove that `(w-alpha_1)/(w^2-alpha_1).(w-alpha_2)/(w^2-alpha_2).(w-alpha_3)/(w^2-alpha_3).(w-alpha_4)/(w^2-alpha_4)=w` where w is a nonreal complex cube root of unity.

If z^(2)(bar(omega))^(4)=1 where omega is a nonreal complex cube root of 1 then find z .

If 1,alpha_(1),alpha_(2),alpha_(3),alpha_(4) be the roots x^(5)-1=0 then value of -alpha_(2)(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 1,alpha_(1),alpha_(2),alpha_(3),alpha_(4) are the fifth roots of unity then sum_(i=1)^(4)(1)/(2-alpha_(i))=

If 1,alpha_(1),alpha_(2),alpha_(3),...,alpha_(n-1) are n, nth roots of unity, then (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))...(1-alpha_(n-1)) equals to

If alpha_(1) , alpha_(2) , alpha_(3) , alpha_(4) are the roots of the equation 3x^(4)-(l+m)x^(3)+2x+5l=0 and sum alpha_(1)=3 , alpha_(1)alpha_(2)alpha_(3)alpha_(4)=10 then (l,m)

If alpha_(1),alpha_(2),alpha_(3),alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 then find the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4))

If alpha_(1),alpha_(2),alpha_(3)......alpha_(n) are roots of the equation f(x)=0 then (-alpha_(1),-alpha_(2),-alpha_(3),......alpha_(n)) are the roots of

If 1,alpha_1,alpha_2,alpha_3,.........,alpha_(3n) be the roots of the eqution x^(3n+1) - 1 =0, and w be an imaginary cube root of unity, then ((w^2-alpha_1)(w^2-alpha_2)....(w^(3n)-alpha_(3n))) /((w-alpha_1)(w2-alpha)....(w-alpha_(3n)))

If alpha is a root of x^(3)-x-1=0, compute the value of alpha^(10)+2 alpha^(8)-alpha^(7)-3 alpha^(6)-3 alpha^(5)+4 alpha^(4)+2 alpha^(3)-4 alpha^(2)-6 alpha

If 1,alpha,alpha^(2),……….,alpha^(n-1) are n^(th) root of unity, the value of (3-alpha)(3-alpha^(2))(3-alpha^(3))……(3-alpha^(n-1)) , is