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2. Homework Equations

We studied factional linear transformations with T(z) = (a z + b) / (c z + d) , but I can't seem to apply that here.

We defined the principal branch in the beginning of the class as -Pi < arg z < Pi

We have not discussed the slit along the segment from 0 to i, but I'm guessing the it is like a period strip from Im w = 0 to Im w = i

3. The Attempt at a Solution

I let z = x + iy, but don't know how to work with the sqrt root to get something I can work with.