# Iteration of complex maps

- Author:
- a.zampa

This applet shows the iteration of complex maps of type , were , as a generalization of the concepts discussed in the previous chapters.
Complex numbers , for , may be introduced as numbers needed to solve equations of degree 2, , when their discriminant is negative: there exist no real number whose square is negative, so we "invent" a new number, , such that its square equals , i.e. . Using this definition and algebraic properties, it is easy to find rules for mathematical operations on complex numbers (conjugation and modulus are used to define the reciprocal number and, therefore, division):
is defined in terms of two real numbers, it can be represented by a point on the plane: its abscissa is the and its ordinate is the ).

- Addition:
- Subtraction:
- Multiplication:
- Conjugation:
- Modulus:
- Reciprocal number:
- Division:

*real part*of*immaginary coefficient*(the*immaginary part*beingThe Graphics view displays the first 56 iterations of the map starting with .
Interesting questions are:

- What happens changing values of
and ? - Given the initial value
, for which value of the set of iterates is bounded?