If `alpha and beta` are the complex cube roots of unity, show that `alpha^4+beta^4 + alpha^-1 beta^-1 = 0.`

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

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 imaginary cube root of unity then prove (alpha)^4 + (beta)^4 + (alpha)^-1 . (beta)^-1 = 0

If x=a + b, y= a alpha + b beta, z= a beta + b alpha , where alpha and beta are complex cube roots of unity, then show that xyz = a^(3) + b^(3)

If x = a + b , y = a alpha + b beta , z = a beta + b alpha where alpha and beta are complex cube roots of unity , show that x^(3) +y^(3) + z^(3) = 3 (a^(3)+ b^(3))

If alpha and beta are the roots of a quadratic equation such that alpha+beta=2, alpha^4+beta^4=272 , then the quadratic equation is

If alpha , beta are the roots of ax ^2 + bx +c=0 then alpha ^5 beta ^8 + alpha^8 beta ^5=

If alpha , beta are the roots of x^2 +x+1=0 then alpha beta + beta alpha =

If alpha and beta are different complex numbers with |beta|=1, then find |(beta-alpha)/(1- baralphabeta)| .

If alpha and beta are different complex numbers with |beta|=1, then find |(beta-alpha)/(1- baralphabeta)| .