I am studying maths at A-level, in case that affects the level of explanations.
In a Cartesian plane, a circle with centre $(a,b)$ and radius $r$ is defined as $(x-a)^2 + (y-b)^2 = r^2$. If $r^2$ is negative, is this still an equation of a circle? Is it at all meaningful to have a circle with a complex radius?