complex iteration (complex "height")

[bo198214]

Since I still can not iterate complex numbers, let me make a few opportunistic wild quesses which look nice

\( {1/e}[4]{-\Omega}=\Omega+I*(1-\Omega)=0.567143+I*0.432857... \)

\( {1/e}[4]{-1/\Omega} = \Omega+ I*{(1/\Omega}-1)=0.567143+I*0.763224.. \)

\( {1/e}[4]{\Omega}=\Omega+I*\Omega^{1/(1-\Omega)}=0.567143+I*0.26975. \)


If one of them is close, even real or imaginary part?.

No, quite wrong guesses:
\( \begin{align*}
\frac{1}{e}[4](-\Omega)&=0.4035614-0.4516711*I\\
\frac{1}{e}[4]\frac{-1}{\Omega}&=1.0316317+1.0778810*I\\
\frac{1}{e}[4]{\Omega}&=0.4921705+0.2519841*I
\end{align*} \)