Fun Imaginary Problem

I came across this on Instagram the other day, so props to the creator although I’ve forgotten their username. It was definitely a fun solve.

$(\sqrt[\pi]{i^i})^{-2} = e$

HINT: Use the famous rule from the guy who proved the Konigsberg 7-bridge challenge impossible (or, the second best mathematician in history). See more about this mathematical debut here.

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Beware that a spoiler solution is below.

SPOILER:

Takes me back to the good old days of algebra.