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, 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_(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_1,alpha_2,alpha_3,alpha_4 be the roots x^5-1=0 , then value of [omega-alpha_1]/[omega^2-alpha_1].[omega-alpha_2]/[omega^2-alpha_2].[omega-alpha_3]/[omega^2-alpha_3].[omega-alpha_4]/[omega^2-alpha_4] is (where omega is imaginary cube root of unity)

If alpha_(1), alpha_(2), alpha_(3), beta_(1), beta_(2), beta_(3) are the values of n for which sum_(r=0)^(n-1)x^(2r) is divisible by sum_(r=0)^(n-1)x^(r ) , then the triangle having vertices (alpha_(1), beta_(1)),(alpha_(2),beta_(2)) and (alpha_(3), beta_(3)) cannot be

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 sin (3alpha) /cos(2alpha) < 0 If alpha lies in

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

if [ ( cos alpha, - sin alpha),(sin alpha, cos alpha)] and A +A^1 =I then alpha =……

(sin(3alpha))/(1+2cos(2alpha))= ..........