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 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_(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 z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

If 1,omega,omega^(2),...omega^(n-1) are n, nth roots of unity, find the value of (9-omega)(9-omega^(2))...(9-omega^(n-1)).

For a positive integer n , find the value of (1-i)^(n)(1-(1)/(i))^(n)

If sum_(i=1)^(2n)cos^(-1)x_i=0 then find the value of sum_(i=1)^(2n)x_i

If a_(1),a_(2),a_(3),a_(4) and a_(5) are in AP with common difference ne 0, find the value of sum_(i=1)^(5)a_(i) " when " a_(3)=2 .

If Sigma_( i = 1)^( 2n) sin^(-1) x_(i) = n pi , then find the value of Sigma_( i = 1)^( 2n) x_(i) .

If ,Z_1,Z_2,Z_3,........Z_(n-1) are n^(th) roots of unity then the value of 1/(3-Z_1)+1/(3-Z_2)+..........+1/(3-Z_(n-1)) is equal to

If alpha,beta be the roots of the equation 3x^2+2x+1=0, then find value of ((1-alpha)/(1+alpha))^3+((1-beta)/(1+beta))^3