Complex quadratic polynomial

A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers.

When the quadratic polynomial has only one variable (univariate), one can distinguish its 4 main forms:

The monic and centered form has the following properties:

Since ${\displaystyle f_{c}(x)\,}$ is affine conjugate to the general form of the quadratic polynomial it is often used to study complex dynamics and to create images of Mandelbrot, Julia and Fatou sets.

When one wants change from ${\displaystyle \theta \,}$ to ${\displaystyle c\,}$:

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