If `x=a+b,y=a alpha+b beta and z=abeta+ b alpha` , where `alpha and beta` are the imaginary cube roots ofunity, then `xyz=`

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))

Find the equation whose roots are (alpha)/(beta) and (beta)/(alpha) , where alpha and beta are the roots of the equation x^(2)+2x+3=0 .

If alpha , beta , gamma in {1,omega,omega^(2)} (where omega and omega^(2) are imaginery cube roots of unity), then number of triplets (alpha,beta,gamma) such that |(a alpha+b beta+c gamma)/(a beta+b gamma+c alpha)|=1 is

If at a nalpha+bt a nbeta=(a+b)tan((alpha+beta)/2) , where alpha!=beta , prove that acosbeta=bcosalphadot

If 0 gt a gt b gt c and the roots alpha, beta are imaginary roots of ax^(2) + bx + c = 0 then

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

Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2 , where a ,b , in R and beta=(z-1)//(z+1), w here |z|=1, then find the correct statement: both alphaa n dbeta are purely real both alphaa n dbeta are purely imaginary alpha is purely real and beta is purely imaginary beta is purely real and alpha is purely imaginary

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

If 0 lt c lt b lt a and the roots alpha, beta the equation cx^(2)+bx+a=0 are imaginary, then