I came across this question which I successfully solved computationally, but I was wondering if there is an analytical way of doing it.
Find Real and Imaginary parts of: $$ i^{i^{i^{i^{.^{.^ {2019}}}}}}$$
From Anas's comment it can be written as:
$${}^{2019} i$$
It also could be written as:
$i^{(i)^i} $ and so on till there are 2019 $i's$.
PS: I couldn't continue in this fashion further to show till 2019.