Now that I know that the branch points of a function $\sqrt[n]{P(z)}$ can be determined by the integral division of the zero points of $P(z)$ by n.
Then how to find the branch points of this logarithmic function on a complex domain: $Ln(P(z))$, where $P(z)$ is a polynomial function like $z^3+2z^2+5 ...$, and $Ln(z)=ln|z|+iArgz,z\in\mathbb{C}$.
For example, branch points of $Ln(1-z^2)$ are $-1,+1,\infty$