$$f(\alpha)=\alpha$$
$\left\{\begin{matrix}\\f=1\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&\alpha =0\end{matrix}\right.$
$\left\{\begin{matrix}\\\alpha =0\text{, }&\text{unconditionally}\\\alpha \in \mathrm{C}\text{, }&f=1\end{matrix}\right.$
$\left\{\begin{matrix}\\f=1\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&\alpha =0\end{matrix}\right.$
$\left\{\begin{matrix}\\\alpha =0\text{, }&\text{unconditionally}\\\alpha \in \mathrm{R}\text{, }&f=1\end{matrix}\right.$