I learned about complex numbers after I was trying to create a fractal object.
The main problem is that I have an equation with complex numbers and I have to separate their parts (real & imaginary) to calculate the next iteration.
Some equations like the $f(p) = p^2 + c$ are obviously and easy to solve them. But some of them are using the exponential form of the complex numbers, that really bothers me.
Take for example this equation:
\begin{equation*}
F(P) = c*e^{-p} + p*p~\text{Where}~c = u + v*i~\text{and}~p = a + b*i.
\end{equation*}
I solved it partly by this way - express $e^{-p}$ like $1 / (e^a \ast (\cos(b) + \sin(b) * i))$ and so on... But in the end I couldn't see the relation to separate the groups.
Any help and advice how to proceed in this or similar case will be greatly appreciated.
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