Let `alpha,beta` denote the cube roots of unity other than `1 and alpha!=beta.` Let `S=sum_(n=0)^302(-1)^n(alpha/beta)^n.` Then, the value of `S` is

Let alpha ,beta denote the cube roots of unity other than 1 and alpha ne beta let S=underset(n=0)overset302sum(-1)^n(alpha/beta)^n then the value of S is

Let alpha,beta denote the cube roots of unity other then 1 and let s=underset(n=0)overset(302)sum(-1)^(n)((alpha)/(beta))^(n) . Then the value of s is -

If alpha and beta are complex cube roots of unity, show that alpha^2 + beta^2 + alpha beta =0

If alpha , beta be the imaginary cube root of unity, then show that alpha^4+beta^4+ alpha^-1beta^-1=0

If alpha,beta be the imaginary cube root of unity, then the value of (alpha^4+alpha^2beta^2+beta^4) is

If alpha,beta are the complex cube roots of unity then alpha^(100)+beta^(100)+(1)/(alpha^(100)xx beta^(100))=

If alpha and beta are the complex cube roots of unity, then prove that (1 + alpha) (1 + beta) (1 + alpha)^(2) (1+ beta)^(2)=1

If alpha and beta are the complex cube roots of unity, then prove that (1 - alpha) (1 - beta) (1 - alpha^2) (1 - beta^2) = 9 .