# How to find branch point of $z^z$

Regarding question relating to branches as shown below:

Consider the multi-valued operation $z^z$. How do I find the branch points and all its possible value at $z=1$?

Thanks for helping me everybody

The only possible value is $1$, since $1^1=\exp(1\times\log 1)$, where $\log(1)$ is some logarithm of $1$. But the logarithms of $1$ are the numbers of the form $2k\pi i$ ($k\in\mathbb Z$), and therefore, as I wrote, $1^1=\exp(2k\pi i)=1$.
• @john If $z=1$, yes. Otherwise, it depends upon the number. – José Carlos Santos Sep 26 '17 at 13:51