DearMHFusers,

let $\displaystyle \varphi:\mathbb{N}\to\mathbb{R}$ be a function and $\displaystyle n\in\mathbb{N}$.

For $\displaystyle z\in\mathbb{C}$ define a function $\displaystyle \Phi:\mathbb{C}\to\mathbb{C}$ by

$\displaystyle \Phi(z):=\prod_{k=1}^{n}\big(1+\varphi(k)z\big)$.

How can I decompose this type of functions into itsrealandimaginaryparts?