Complex Numbers as Vectors

Complex numbers as vectors is part of the Complex numbers topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-03). Each complex number can be drawn as a vector from the origin, with length equal to its modulus and direction set by its argument; adding or subtracting complex numbers then follows the usual vector rules on the Argand diagram.

Students and teachers will cover how multiplying by \(i\) or by \(r\operatorname{cis}\theta\) gives a rotation and dilation, and how to use this to prove facts about squares, rectangles and special triangles — linking complex arithmetic with geometry in the HSC Extension 2 course.