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). This subtopic defines the number \(i\) by \(i^2 = -1\), defines the complex numbers as numbers of the form \(a + ib\), and uses them to express the roots of quadratic equations with a negative discriminant.

Students and teachers will cover the real and imaginary parts \(\operatorname{Re}(z)\) and \(\operatorname{Im}(z)\), addition, subtraction and multiplication, the complex conjugate \(\bar{z} = a - ib\), the modulus \(|z| = \sqrt{a^2+b^2}\), division, and finding the two square roots of a complex number — the algebraic foundation for the HSC Extension 2 course.