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

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

if alpha and beta are imaginary cube root of unity then prove (alpha)^(4)+(beta)^(4)+(alpha)^(-1)*(beta)^(-1)=0

If a and b are imaginary cube roots of unity, then alpha^(n)+beta^(n) is equal to

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 be the roots of the equation x^2-1=0 , then show that. alpha+beta=(1)/(alpha)+(1)/(beta)

If alpha,beta are the roots of 1+x+x^(2)=0 then the value of alpha^(4)+beta^(4)+alpha^(-4)beta^(-4) =

If alpha and beta are the complex cube roots of unity, then what is the vlaue of (1+alpha)(1+beta)(1+alpha^(2))(1+beta^(2)) ?

If alpha, beta, gamma are cube roots of unity, then the value of |(e^(alpha),e^(2alpha),(e^(3alpha)-1)),(e^(beta),e^(2beta),(e^(3beta)-1)),(e^(gamma),e^(2gamma),(e^(3gamma)-1))|=