Let integers \( a,b\in[-3,3] \) be such that \( a+b\ne 0 \). Then the number of all possible ordered pairs \( (a,b) \), for which \( \left|\dfrac{z-a}{\,z+b\,}\right|=1 \) and 
, where \( \omega \) and \( \omega^2 \) are the roots of \( x^2+x+1=0 \), is equal to ________.
