I'm taking the complex variable course and I find the Wolfram Alpha website very helpful for me to understand the Riemann surface.
For example typing "Riemann surface z^(1/2)" I get nice plots
but when I try (z+1)^(1/2)+(z-1)^(1/2), I get something like this:
As I understand, the branch cut happens at $(-\infty,-1)$ and $(1,\infty)$, then why there are cuts between -1 and 1 in the plot? Did I make a stupid mistake?