[Solved] Let \\omega = e^{\\frac{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. Ten the value of \\frac{\\mid x \\mid^2 + \\mid y \\mid^2 + \\mid z \\mid^2}{\\mid a \\mid^2 + \\mid b \\mid^2 + \\mid c \\mid^2} is - - JEE (Advanced) 2011 Paper-2