Colorful visualization of complex functions

A short introduction with lots of examples

hun eng

Linear

See below the plot of a linear function.

Linear function Coloring

\(f(z) = (2+i)z + 2,\quad z \in \mathbb{C}(0,3)\)

It can be deduced in a few lines that complex linear functions as geometric transformations can be reproduced as the composition of dilation, rotation and translation. This is very well reflected on this figure.

We might want to calculate where the zero of the function is. The result of a correct calculation would be in accordance with this picture.

We might rephrase that 'and this can be seen very nicely on this picture' in the case of every plot we will show. From now on we will avoid this but one should be encouraged to always recall that thought.

Developed by: Levente Lócsi (ELTE IK NA / EJC IM) at NuHAG in May 2011. Valid XHTML and CSS.