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I want to find all the set of values for the expression $i^{i^i}$.

For the principal value of this expression I got $e^{i\frac{\pi}{2}}e^{e^{-\frac{\pi}{2}}}$, please correct me if wrong.

Any hints or help would be appreciated.

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    $\begingroup$ I believe the principal value would actually be $e^{i\frac{\pi}{2}e^{-\pi/2}}=0.947+0.321i$. $\endgroup$ – Jam Nov 23 '19 at 18:11
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Use the fact $i=e^{\ln i}$ and $\ln i=i\frac{\pi}{2}+i(2\pi n) \forall n\in \mathbb{Z}$ . Can you go from gere$?$

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  • $\begingroup$ Well, but I get 2 parameters $n\in\mathbb{Z}$. One for each of the powers. I guess I have to define 2 parameters $n,n’$ and define the set of values in terms of that, right? $\endgroup$ – Phil Mett Nov 23 '19 at 17:55
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    $\begingroup$ @PhilMett That's correct. There are two multivalued operations so there's two sets of integers indexing the set of values. $\endgroup$ – Jam Nov 23 '19 at 18:05

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