Describing Lines, Curves & Regions

Describing lines, curves and regions completes the Complex numbers topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-03). This subtopic graphs vertical and horizontal lines \(\operatorname{Re}(z) = c\) or \(\operatorname{Im}(z) = k\), the line \(|z - z_1| = |z - z_2|\), circles \(|z| = r\) and \(|z - z_1| = r\), and rays \(\arg(z) = \theta\) on the complex plane.

Students and teachers will cover how to graph regions defined by combinations of these lines, rays and circles and give a geometrical description of each locus, using circle-geometry theorems where necessary — a heavily illustrated part of the HSC Extension 2 course.