Complex quadratic polynomial

Definition

Complex quadratic polynomial is quadratic polynomial which parameters (coefficients ) and variable are complex numbers.

Special cases

Monic complex quadratic polynomial  :
$P_{c}(z)=z^{2}+c\,$
is very important in the theory of dynamical systems.
It is a simplest form of nonlinear function of one variable $z\,$ and one parametr $c\,$.
When it creates discrete dynamical systems
$z_{n+1}=P_{c}(z_{n})=z_{n}^{2}+c\,$
it is named quadratic map.