If `1, alpha and alpha^(2)` be three cube roots of 1 and `x=a+b,ya+balpha,z=a+balpha^(2) and x^(3)+y^(3)+z^(3)=K(a^(3)+b^(3))`, then the value of K is

If z=x+i y, z^(1 / 3)=a-i b and (x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then the value of k=

If alpha,beta are complex cube roots of unity and x=a+b , y=aalpha+bbeta , z=abeta+balpha , then the value of (x^(3)+y^(3)+z^(3))/(xyz) is:

If omega be a complex cube root of unity and x=alpha+beta,y=alpha+beta omega, z=alpha + beta omega^(2), show that, x^(3)+y^(3)+z^(3)=3(alpha^(3)+beta^(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))

z=x+iy,z^(1/3)=a-ib,(x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then k is :

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

If x:y=2:3 , y:z=3:4 , z:k=1:2 , find the value of x:y:z:k

IF lines (x-1)/(2) =(y+1)/(3) =(z-1)/(4) and x-3 =(y-k) /(2) = z intersect then the value of k is