If `1,alpha_(1),alpha_(2)......alpha_(n-1)` are `n^(th)` roots of unity then `(1)/(1-alpha_(1))+(1)/(1-alpha_(2))+......+(1)/(1-alpha_(n-1))=`

if alpha_(1),alpha_(2),.... alpha_(8) are the 8 th roots of unity then:

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 1,alpha_(1),alpha_(2),………..,alpha_(n-1) are nk^(th) roots of unity, then the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))……(1-alpha_(n-1)) is equal to

If 1,alpha_(1),alpha_(2),...,alpha_(n-1) are the nth roots of unity,prove that (1-alpha_(1))(1-alpha_(2))...(1-alpha_(n-1))=n. Deduce that sin(pi)/(n)sin(2 pi)/(n)...sin((n-1)pi)/(n)=sin(n)/(2^(n-1))

If 1,alpha,alpha^(2),alpha^(3),......,alpha^(n-1) are nn^(th) roots of unity,then find the value of (2011-alpha)(2011-alpha^(2))....(2011-alpha^(n-1))

If 1,alpha_1, alpha_2, …alpha_(n-1) be n, nth roots of unity show that (1-alpha_1)(1-alpha_2).(1-alpha(n-1)=m

1,alpha_(1),alpha_(2),..... alpha_(9), are the 10^(th) roots of unity. The product (2 alpha_(1)+1)(2 alpha_(2)+1)......(2 alpha_(9)+1) equals a reduced rational number (m)/(n) the value of m+n is

If nge3and1,alpha_(1),alpha_(2),.......,alpha_(n-1) are nth roots of unity then the sum sum_(1leiltjlen-1)alpha_(i)alpha(j)=