# Argand diagrams

Level: A Level Maths

An Argand diagram is a way of representing complex numbers on a diagram.

## Complex numbers in 2 dimensions

A real number can be represented as a point on a number line.

Since a complex number has two components (the real part and the imaginary part), it cannot be represented as a point on a line, but instead it can be represented as a point on a plane.

## Argand diagram

In an Argand diagram, we represent a complex number:

$z=x+iy$ as a point $(x,y)$ on a graph using Cartesian coordinates.

The $x$ coordinate represents the real value, so the x-axis is called the real axis. The $y$ coordinate represents the imaginary value, so the y-axis is called the imaginary axis.

In this diagram:

• Point A, with an $x$ value of 4 and a $y$ value of 3, represents the complex number $4+3i$ .
• Point B, with an $x$ value of -2 and a $y$ value of 3, represents the complex number $-2+3i$ .
• Point C, with an $x$ value of -3 and a $y$ value of -1, represents the complex number $-3-i$ .