Complex numbers

Loci and transformations

$|z-a|=r$ is a circle and $|z-a|=|z-b|$ a perpendicular bisector; $|z-a|=k|z-b|$ ($k\neq1$) is a circle of Apollonius. A function $w=f(z)$ maps the $z$-plane to the $w$-plane: write $z$ in terms of $w$, substitute into the locus, and simplify.