I’m doing exercises about branch-cut. It really confuses me about the difference between, for example, $\sqrt{z(z-1)}$ and $\sqrt{z(1-z)}$, because the solutions are seemingly the same all the time!
It would be greatly appreciated if you could kindly tell me what I might have missed.
When looking for branches, we look at where the function is discontinuous. This happens in the following cases. When $z(z-1)<0$ we see that $0<z<1$ is part of some branch. When $z(1-z)<0$ we see that $z>1$ is part of some branch.