Just covered branch cuts in my undergraduate course but stuck on one of the questions...

Find the domain on which f(z) = arccot(z) is single valued and analytic.

Now, we've looked at ln(z) in class and I understand the principal of limiting the domain but i'm not having much success and see no examples anywhere on the internet.

Some pointers would be great or an explanation of how to tackle this kind of function.

How I thought I may start is:

Let w = cot(z) and in exponential form $\displaystyle i* \frac{\exp{(iz)}+\exp{(-iz)}}{\exp{(iz)}-\exp{(-iz)}} $

Then let $\displaystyle y = \exp{iz} $ so you get:

$\displaystyle w = i* \frac{y+y^{-1}}{y-y^{-1}} $

I though i might be able to solve the last equation but I'm not sure now.

anyway, if you could point me in the right direction I'd be most thankful....

D