Find all roots tanh(z)=i
tanhz = [e^(z)-e^(-z)]/[e^(z)+e^(-z)]
where do i go from here?
At this level of mathematical studies you should have seen the following steps (*):
$\displaystyle e^z - e^{-z} = i \left( e^z + e^{-z}\right)$
* $\displaystyle \Rightarrow e^z - e^{-z} = i e^z + i e^{-z}$
* $\displaystyle \Rightarrow e^z - i e^z = e^{-z} + i e^{-z}$
$\displaystyle \Rightarrow (1 - i) e^z = (1 + i) e^{-z}$