# Is the Riemann surface plot in Wolfram Alpha wrong?

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?

• Isn't the entire point of Riemann surfaces that there is no branch cut because there is an entire surface - and the point of a branch cut to change a surface into the graph of a function? Commented Sep 9, 2013 at 23:24
• @CarlMummert I'm sorry that I don't see your point. I agree that the Riemann surface is an entire surface, and branch cut is the place that Riemann sheets cross, but how does that relate to the question? Commented Sep 9, 2013 at 23:56
• I can't make heads or tails of that surface. Did you compare it to the surface of the product $\sqrt{z-1}\sqrt{z+1}$ ? That one should really be a cut between $-1,1$. When I did it on wolfram alpha it seems to be different.
– Evan
Commented Sep 10, 2013 at 0:06