In this problem we have two selected points in the complex plane: A = (-2,0) 
and B = (2,0).


The complex number z-2 represents a vector connecting point z with the point (2,0).


The complex number z+2 represents a vector connecting point z with the point (-2,0).


Since   =   (given), it means that the angle between the vectors  (z-2)  and  (z+2)  is  .


It means that the point z lies on the arc of a circle and the vectors (z-2) and (z+2)  form an inscribed angle  

of the measure of   = 60 degrees, which leans on the segment AB as on the chord.



The locus is shown in the Figure below in red line.


    The parts of the circles shown in black are not the parts of the locus.