Let `omega =e^(ipi/3) and a,b,c,x,y,z ` be nonzero complex number such that `a+b+c=x, a+bomega+comega^2=y, a+bomega^2+comega=z`. Then the value of `(|x|^2+|y|^2+|z|^2)/(|a|^2+|b|^2+|c|^2)` is

Let omega=e^((i pi)/(3)) and a,b,c,x,y,z be non-zero complex numbers such that a+b+c=x,a+b omega+c omega^(2)=y,a+b omega^(2)+c omega=z Then,the value of (|x|^(2)+|y|^(2)|+|y|^(2))/(|a|^(2)+|b|^(2)+|c|^(2))

If =a+b,y=aomega+bomega^2 and z=aomega^2+bomega, prove tht xyz=a^3+b^3

If omega be an imaginary cube root of unity, show that (a+bomega+comega^2)/(aomega+bomega^2+c) = omega^2

Show that |a b c a+2x b+2y c+2z x y z|=0

If omega is a cube root of unity, prove that (a+bomega+comega^2)/(c+aomega+bomega^2)=omega^2