What are the branch points of the function w(z)=arctan(z)

Question

I have the next question:
What are the branch points of the function $w(z)=\arctan(z)$.
I don't have any idea of how to start to solve this question.

Can someone please guide me on how to approach this question? Thank you very much in advance.

Answer 1

They did just algebra:

$$iz=\frac{e^{2iw}-1}{e^{2iw}+1}\stackrel{\text{common denominator}}\implies(iz-1)e^{2iw}=-iz-1\implies e^{2iw}=\frac{1+iz}{1-iz}$$