Further Maths
Complex numbers become clearer when algebra meets geometry.
This prototype uses an Argand diagram to connect complex numbers with modulus, argument, conjugates, multiplication and roots of unity.
The aim is to help learners see multiplication as rotation and scaling, rather than only as algebraic expansion.
Argand diagram lab
See complex numbers as points, vectors and rotations
Move z on the Argand diagram, multiply it by a complex number in polar form, and compare the result with its modulus, argument and conjugate.
z
1.6 + 1.1i
|z|
1.94
arg(z)
34.51 deg
zw
0.44 + 2.39i
Joy in the process
The point is not just to finish. It is to notice, test and return.
These tools are invitations to explore. A good mistake, a surprising pattern or a question you cannot yet answer is part of the work, not a failure of it.
The challenge is deliberate: the site should support thinking, not remove the need for it.
Before changing a setting, pause and predict what you think will happen.
Change one thing at a time. What stayed the same, and what changed?
Try to create a surprising case, a broken case, or a beautiful pattern.
Ask what this connects to outside the page: maps, movement, nature, systems or decisions.
Reset, then try again with a new question in mind.
Future extensions
This can grow into a full complex numbers playground.
Add draggable points directly on the Argand diagram.
Add De Moivre's theorem and powers of complex numbers.
Add roots of complex numbers beyond roots of unity.
Add challenge mode: match a target rotation, modulus or argument.