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

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_(4) are the fifth roots of unity then sum_(i=1)^(4)(1)/(2-alpha_(i))=

If 1,alpha,alpha^2,…,alpha^(n-1) are the n^(th) roots of unity show that sum_(r=1)^(n-1)r(alpha_r+alpha_(n-r))=-n .

If 1,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)(1)/(2-a_(i)).

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)(1)/(2-a_(i)).

If 1,alpha_1,alpha_2,…..alpha_(n-1) are the n^(th) roots of unity then (1-alpha_1)(1-alpha_2)…..(1-alpha_(n-1))=

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-alpha_(i)).

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 1, alpha,alpha^2.......alpha^(n-1) are the nth roots of unity then prove that (1-alpha)(1-alpha^2).....(1-alpha^(n-1))=n