Find a conformal map of the slit plane $\displaystyle \mathbb{C} \backslash (-\infty, 0]$ onto the open unit disk satisfying $\displaystyle w(0)=i, w(-1+0i)=+1, w(-1-0i)=-1$. What are the images of circles centered at 0 under the map? Sketch them.

The back of the book says that $\displaystyle w=\frac{-i(\sqrt{z}-1)}{\sqrt{z}+1}$ works. I think for the second part of the question I can consider three points on the circles to find the images. However, I don't see how they found this map. Thanks.