Find an analytic function that maps the plane with the slit $[-1,1]$ onto the upper half plane
Normaly I can find the function from $3$ points easily, but this problem doesn't give me any point. So I know that $z$ is in the plane that delete the line segment on the real aaxis from $-1$ to $1$ and I know that the image is only cover the upper half plane, so I guess $f(z)$ must have $z^2$ in it? or the whole expression is square?
However, these infor is not enough for me to get the 3 points, I wonder if anyone would please give me a hint.