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 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_(n-1) are the n^(text (th ) roots of unity and n is odd natural number, then (1+alpha_(1))(1+alpha_(2)) ... . .(1+alpha_(n-1))=

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

If alpha is a non-real fourth roots of unity, then the values of alpha^(4 n-1)+alpha^(4 n-2)+alpha^(4 n-3), n in N is

If sin alpha , 1 , cos 2 alpha are in GP, then find the general solution for alpha

If alpha is an imaginary fifth root of unity then log _(2)|1+alpha+alpha^(2)+alpha^(3)-(1)/(alpha)|=

If alpha,beta and gamma are roots of x^(3) -2x+1=0,then the value of Sigma((1)/(alpha+beta-gamma)) is

If a_(1),a_(2),".....", are in HP and f_(k)=sum_(r=1)^(n)a_(r)-a_(k) , then 2^(alpha_(1)),2^(alpha_(2)),2^(alpha_(3))2^(alpha_(4)),"....." are in {" where " alpha_(1)=(a_(1))/(f_(1)),alpha_(2)=(a_(2))/(f_(2)),alpha_(3)=(a_(3))/(f_(3)),"....."} .

If A=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then verify that A'A=I

If A=[(sin alpha, cos alpha),(-cos alpha, sin alpha)] , then verify that A'A=I