Solution
= Solution
The slit plane is connected and contains $D$. If two <holomorphic functions> on it extend the same $f$, their difference vanishes on the nonempty open disc $D$. The <identity theorem> forces their difference to vanish on the entire slit plane. Thus \b[there is at most one analytic extension of the chosen $f$]. Choosing the opposite square root initially changes that chosen function; it does not produce two extensions of the same function.