We define the principal branch of the inverse tangent function by,
$\displaystyle Arctan(z) = \frac{i}{2}\log(\frac{i+z}{i-z}$)
For which values of z is Arctan(z) defined?
The function $\displaystyle \tan^{-1} z = \frac{i}{2} \ln \frac{i+z}{i-z}$ is defined for all $\displaystyle z \in \mathbb{C}$ with the only exceptions of the points $\displaystyle z=i$ and $\displaystyle z=-i$, that represent the 'singularities' of the function ...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$
No, for beeing log z well defined, and analytic, we need eliminate a branch
(line beginning from 0). So, if nothing else is especified, logz is defined in
C\[0,\infty). You need to solve the equatiom
$\displaystyle \arg\frac{i+z}{i-z}=\pi$
to obtain the correct domain of definition.