The locus of z when |z-z_1| < a, where a is a fixed constant and z_1 is a fixed known complex number.
If z=x+iy is represented on an Argand diagram by the vector going from the origin to the point P with coordinates (x,y), and z_1 = x_1+iy_1 is a known complex number represented by the vector OQ where Q has coordinates (x_1,y_1), then the equation |z - z_1| < a requires the distance of P from Q to be at most a units. So the locus is the interior of a circle, centre (x_1,y_1), with radius a units. In the diagram below you can vary the value of a and the vector z_1. Clearly, P must lie within the circle shown.