Roots of Complex Numbers

Roots of complex numbers is part of the Complex numbers topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-03). This subtopic solves equations such as \(z^n = 1\), \(z^n = -1\) and \(z^n = w\) using polar form, finding all \(n\) solutions and plotting them on the Argand diagram.

Students and teachers will cover why the \(n\)th roots of unity sit evenly spaced around the unit circle and form a regular polygon, why they add to zero, and how to use roots of complex numbers in problems and proofs — an elegant blend of algebra and geometry in the HSC Extension 2 course.