Let  $A\left({\omega }^2\right)$ , $B\left(2i\omega \right)$  and C(-4) be three points lying on the Argand plane. Now a point P is taken on the circumcircle of the triangle ABC such that PA. BC = PC. AB, (where P, A, B, C are in order). If z is the complex number associated with the mid – point of PB, then the value of ${\left|Z\right|}^2$  is, ( $\omega$ is a non – real cube rot of unity)