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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.

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They did just algebra:

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

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  • $\begingroup$ But how did they came to the expression $(iz-1)e^{2iw}$? $\endgroup$ – violettagold Nov 9 at 12:35
  • $\begingroup$ @violettagold That is simple high school algebra...try to do it! It involves what is written there and and common factoring out...If you attempt to do complex analysis this must, really must, be a piece of cake. $\endgroup$ – DonAntonio Nov 9 at 12:42

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