Arithmetic of Complex Numbers

Arithmetic of complex numbers introduces the Complex numbers topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-03). Starting from \(i^2 = -1\), this subtopic builds the complex numbers \(z = a + ib\) with real \(a\) and \(b\), and shows that a quadratic with a negative discriminant still has two solutions once complex values are allowed.

Students and teachers will cover the real and imaginary parts \(\operatorname{Re}(z)\) and \(\operatorname{Im}(z)\), the four operations, powers of \(i\), the conjugate \(\bar{z}\), the modulus \(|z| = \sqrt{a^2+b^2}\), and how to find both square roots of a number such as \(7+24i\) — the algebraic base of the HSC Extension 2 course.