I am self-studying complex analysis with a friend and we are struggling to do the following problem:
Find a biholomorphism from $D = \{z : -a < Re(z) < a \}$ to the unit disk.
Our idea would be to transform it to the upper halfplane first in some way but we're not sure how to do this. Do you have any tricks or hints on how to do this? Is going to the halfplane even the right idea?