I know there is a lot of answers on this forum, but I simply dont understand how to solve:

Find a branch of $\log(z^2 + 1)$ that is analytic at $z=0$ and takes the value $2\pi i$ there.

I simply can't grab this, someone gave a hint to look for branch points, looking of where the function is continous etc. Is there a method that will work everytime and does anyone have the patience to explain the method. Thanks in advance :)


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