If `alpha_(0),alpha_(1),alpha_(2),...,alpha_(n-1)` are the n, nth
roots of the unity , then find the value of `sum_(i=0)^(n-1)(alpha_(i))/(2-a_(i)).`

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 nge3and1,alpha_(1),alpha_(2),alpha_(3),...,alpha_(n-1) are the n,nth roots of unity, then find value of (sumsum)_("1"le"i" lt "j" le "n" - "1" ) alpha _ "i" alpha _ "j"

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:

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,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 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 n,n^(th) roots of unity, alpha_(r )=e (i2(r-1)pi)/(n), r=1,2,…n then ""^(n)C_(1)alpha_(1)+""^(n)C_(2)alpha_(2)+…..+""^(n)C_(n)alpha_(n) is equal to :

If 1,alpha,alpha^(2),………..,alpha^(n-1) are the n, n^(th) roots of unity and z_(1) and z_(2) are any two complex numbers such that sum_(r=0)^(n-1)|z_(1)+alpha^(R ) z_(2)|^(2)=lambda(|z_(1)|^(2)+|z_(2)|^(2)) , then lambda=

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_(s) are ninth roots of unity (taken in counter -clockwise sequence in the Argard plane). Then find the value of |(2-alpha_(1))(2-alpha_(3)),(2-alpha_(5))(2-alpha_(7)) |.