# 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:

${\displaystyle z=x+iy}$

as a point ${\displaystyle (x,y)}$ on a graph using Cartesian coordinates.

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

In this diagram:

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