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

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.

• – DonAntonio Nov 8 at 16:06
• In the solution, they have done: $iz=\frac{e^{2iw}-1}{e^{2iw}+1}\Rightarrow e^{2iw}=\frac{iz+1}{1-iz}$ . How did they do that? – violettagold Nov 8 at 16:59

$$iz=\frac{e^{2iw}-1}{e^{2iw}+1}\stackrel{\text{common denominator}}\implies(iz-1)e^{2iw}=-iz-1\implies e^{2iw}=\frac{1+iz}{1-iz}$$
• But how did they came to the expression $(iz-1)e^{2iw}$? – violettagold Nov 9 at 12:35