Solving Equations & the Conjugate Root Theorem

Solving equations and the conjugate root theorem is part of the Complex numbers topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-03). This subtopic solves and factorises quadratic and higher-degree equations over the complex numbers, noting that a quadratic with real coefficients and no real roots has two roots that are conjugates of each other.

Students and teachers will cover the conjugate root theorem — for a polynomial with real coefficients, non-real roots come in pairs \(z\) and \(\bar{z}\) — with its proof, and how to use one known complex root to find the other roots or unknown coefficients in the HSC Extension 2 course.