nth roots of Unity

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

If omega!=1. is nth root of unity,and (omega+x)^(n)=1+bar(omega)+(n-1)/(2n)bar(omega)^(2)+... then value of x

If omega be a nth root of unity, then 1+omega+omega^2+…..+omega^(n-1) is (a)0(B) 1 (C) -1 (D) 2

If omega is a complex nth root of unity,then sum_(r=1)^(n)(a+b)omega^(r-1) is equal to (n(n+1)a)/(2) b.(nb)/(1+n) c.(na)/(omega-1) d.none of these

If alpha is the nth root of unity,then 1+2 alpha+3 alpha^(2)+rarr n terms equal to a.(-n)/((1-alpha)^(2)) b.(-n)/(1-alpha^(2)) c.(-2n)/(1-alpha) d.(-2n)/((1-alpha)^(2))

if omega is the nth root of unity and Z_1 , Z_2 are any two complex numbers , then probe that . Sigma_(n-1)^(k=0)| z_1+ omega^k z_2|^2=n{|z_1|^2+|z_2|^2} where n in N

If 1,w,w^2,.....w^(n-1) are then n, nth root of unity, then (2-w)(2-w^2).....(2-w^(n-1)) equals. (i)2^n (ii).^nC_2.....^nC_n (iii)[.^2nC_0+.^(2n+1)C_1+.^(2n+2)C_2...........+.^(2n+2)C_n)]^(1/2) (iv) 2^n+1