A formula for the real part of the product of two complex numbers I have found the following in a paper and I can't see how it is achieved:
$$
    e^{\operatorname{Re}(s\ln u)} = e^{\operatorname{Re}(s)\ln{|u|}-\operatorname{Im}(s)\operatorname{Arg}(u)}
$$
where $u,s \in \mathbb{C}$

Let , $s=s_1+is_2\in \mathbb C$. Also , $\ln u=\ln |u|+i\arg(u)$.
Then , $s\ln u=(s_1\ln|u|-s_2\arg u)+i(s_1\arg u+s_2\ln |u|)$.
So , $\Re(s\ln u)=s_1\ln |u|-s_2\arg u=\Re(s)\ln|u|-\Im(s)\arg(u)$.
