Let z? and z? be two complex numbers satisfying (z-w)+(z-w) = 0, where w is non real cube root of unity. Also let 'a' be

Let z? and z? be two complex numbers satisfying (z-w)²+(z-w²)² = 0, where w is non real cube root of unity. Also let 'a' be a variable point on the circle |z+1/2|=?3/2 and a?, a2 are values of a such that lal is maximum and minimum respectively. On the basis of above information, answer the following questions : Number of complex numbers a such that la - a?l +|a -a?l= ?6 is