If $1, \omega, \omega^2$ are the cube roots of unity and $a, b$ are real and $x = a + b$, $y = a \omega^2 + b \omega$, $z = a \omega + b \omega^2$, then $x^2 + y^2 + z^2$ is equal to :

Question

( A ) $12 ab$
( B ) $4a^2b^2$
( C ) $6 ab$
( D ) $8a^2b^2$