Question

If \(tan (\alpha +i\beta) = e^{i\theta}\)

find
\(\alpha\) and \(\beta\)

Answer 1

will going into hyperbolic tan help ?

\(\tan(\alpha +i\beta) = \dfrac{\tan \alpha +\tan(i\beta)}{1-\tan \alpha \tan (i\beta)} \)

then tan (i beta) can we written in terms of hyperbolic tan
but whats the use

Answer 2

Let's first recall the following: