I've just started adding some basic complex numbers content to the site (definitely feel I've done this before!) My current plan is to add the following content.
|The arithmetic of complex numbers||Yes|
|Roots of quadratics||Yes|
|Roots of polynomials (and the fundamental theory of algebra)|
|symmetric combinations of roots|
|Modulus and Argument||Yes|
|The geometry of complex numbers (and the Argand diagram)||Yes|
|Loci and Transformations||Yes|
After this, I think matrices would be a nice topic to visit.
The fractal image was generated using Ultra Fractal 6. Part of the Mandelbrot set, which is generated by looking at the iterations of points, $c$, in the complex plane under the transformation $z\rightarrow z^2 + c$.