Locus Calculus
posted by Daksh .
Find the equation of the locus of the point representing z if z512i + z5+21i=13

correction:
z512i + z5+12i=13 
z512i is the distance of z from 5+12i
z5+12i is the distance of z from 512i
As we know, the locus of a point whose distances from two other points add to a constant, is an ellipse.
The equation of the ellipse should be no problem, since you know the foci and the sum of the distances.