Complex animation in complex domain

f(z) =

The independent variable must be z, the multication sign must be *. you can send your formula to me for saving it here.

Example:
(z^5-1) (z^(-5)-1) (z-1)/(z+1) z^(1+i) log(z) sin(z) arcsin(z) 2*z+pi/2*(sin(z-i)/sin(z+i))^(1+i) Convergence of Geometric series Julia set Mandelbrot set Newton Newton-like

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