Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 1 / 11 / d / ii

The same completed square gives $|z+b{|}^2=|b{|}^2-c$. A nondegenerate circle therefore occurs exactly whenFor completeness, $c>|b{|}^2$ gives an empty locus because a squared complex modulus cannot be negative.