Well, first, that's not correct. Was that supposed to be "= ", not ">"? I'm going to assume "="
You know, I hope, that the equation of a circle with center (a,b) and radius r is .
Now look at what you are given: |z|^2+ 2Re(az)= -|a|^2. Write z= x+ yi and a= a+ bi (I'm using a to mean to different things but we aren't going to use them in the same equation).
|z|^2= (x+ yi)(x- yi)= x^2+ y^2
az= (a+ bi)(x+ yi)= ax- by+ i(bx+ ay) so 2Re(az)= ax- by.
Finally, |a|^2= (a+bi)(a-bi)= a^2+ b^2.
Sp |z|^2+ 2Re(az)= -|a|^2 becomes x^2+ y^2+ ax- by= -a^2- b^2 which is the same as x^2+ ax+ a^2+ y^2- by+ b^2= 0
Hmmm, (x+a)^2+ (y-b)^2= 0 is NOT the equation of a circle, it is a single point, (-a, b). And keeping the ">" also does not give a circle, it gives every point in the plane except (-a, b).