Argand Diagrams (Cambridge (CIE) A Level Maths) : Revision Note
Did this video help you?
Argand Diagrams - Basics
What is an Argand diagram?
An Argand diagram is a geometrical way to represent complex numbers as either a point or a vector in two-dimensional space
We can represent the complex number
by the point with cartesian coordinate
The real component is represented by points on the x-axis, called the real axis, Re
The imaginary component is represented by points on the y-axis, called the imaginary axis, Im


You may be asked to show roots of an equation in an Argand diagram
First solve the equation
Draw a quick sketch, only adding essential information to the axes
Plot the points and label clearly
How can I use an Argand diagram to visualise |z1 + z2| and |z1 - z2|?
Plot two complex numbers z1 and z2
Draw a line from the origin to each complex number
Form a parallelogram using the two lines as two adjacent sides
The modulus of their sum |z1 + z2| will be the length of the diagonal of the parallelogram starting at the origin
The modulus of their difference |z1 - z2| will be the length of the diagonal between the two complex numbers

Worked Example

Examiner Tips and Tricks
When setting up an Argand diagram you do not need to draw a fully scaled axes, you only need the essential information for the points you want to show, this will save a lot of time.
You've read 0 of your 5 free revision notes this week
Sign up now. It’s free!
Did this page help you?