If `1,alpha_1,alpha_2, ,alpha_(n-1)` are the `n t h` roots of unity, prove that `(1-alpha_1)(1-alpha_2)(1-alpha_(n-1))=ndot` Deduce that `sinpi/nsin(2pi)/n sin((n-1)pi)/n=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 nge3and1,alpha_(1),alpha_(2),.......,alpha_(n-1) are nth roots of unity then the sum sum_(1leiltjlen-1)alpha_(i)alpha(j)=

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

If 1,alpha,alpha^(2),.......,alpha^(n-1) are the n^(th) roots of unity, then sum_(i=1)^(n-1)(1)/(2-alpha^(i)) is equal to:

Let 1, z_(1),z_(2),z_(3),…., z_(n-1) be the nth roots of unity. Then prove that (1-z_(1))(1 - z_(2)) …. (1-z_(n-1))= n . Also,deduce that sin .(pi)/(n) sin.(2pi)/(pi)sin.(3pi)/(n)...sin.((n-1)pi)/(n) = (pi)/(2^(n-1))

Let 1, z_(1),z_(2),z_(3),…., z_(n-1) be the nth roots of unity. Then prove that (1-z_(1))(1 - z_(2)) …. (1-z_(n-1))= n . Also,deduce that sin .(pi)/(n) sin.(2pi)/(pi)sin.(3pi)/(n)...sin.((n-1)pi)/(n) = (pi)/(2^(n-1))

If alpha_1, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_1-alpha_2)(alpha_1-alpha_3)(alpha_1-alpha_n)=n(alpha_1^ n-1+a)

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 alpha_1, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_(1)-alpha_(2))(alpha_(1)-alpha_(3))...(alpha_(1)-alpha_(n))=nalpha_(1)^(n-1)+nalpha