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`

If 1,alpha_1, alpha_2, …alpha_(n-1) be nth roots of unity then (1+alpha_1)(1+alpha_2)……....(1+alpha_(n-1))= (A) 0 or 1 according as n is even or odd (B) 0 or 1 according as n is odd or even (C) n (D) -n

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_(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 n^( th) roots of unity then (1)/(1-alpha_(1))+(1)/(1-alpha_(2))+....+(1)/(1-alpha_(n-1))=

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

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 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

If alpha_(1),,alpha_(2),...,alpha_(n) are the roots of equation x^(n)+nax-b=0, show that (alpha_(1)-alpha_(2))(alpha_(1)-alpha_(2))...(alpha_(1)-alpha_(n))=n(alpha_(1)^(n-1)+a)