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 sketches sets of points on the Argand diagram: lines \(\operatorname{Re}(z) = c\) and \(\operatorname{Im}(z) = k\), the perpendicular bisector \(|z - z_1| = |z - z_2|\), circles \(|z - z_1| = r\), and rays \(\arg(z - z_1) = \theta\).

Students and teachers will cover shading regions formed by combining these conditions, finding a Cartesian equation for each locus, describing each one in words, and using circle-geometry theorems when an argument condition gives an arc — a highly visual part of the HSC Extension 2 course.