Question

I don't get what my Prof did in class. Some one explains me, please.

Answer 1

\[e^{2\pi i}=1\] right?

Answer 2

Problem is not there, that argument is ok, but why it is applied to the equation from the right when \(z_1z_2 \) is arbitrary?

Answer 3

since \(e^{2\pi i}=1\) then \[\log(z_1z_2)=\log(z_1z_2e^{2\pi i})\]

Answer 4

thence \[\log(z_1)+\log(z_2)+\log(e^{2\pi i})\]

Answer 5

I have \(2i n \pi\) , not just \( 2\pi i\).