Imaginary^Imaginary

Algebra Level 4

ii=(eiπ/2)i=eπ/2 i^i = \big(e^{ i \pi / 2} \big)^i = e^{- \pi / 2} It is (initially) surprising that an imaginary number raised to an imaginary number results in a real number.

Characterize all positive kk such that
(ik)ikR. (ik)^{ik} \in \mathbb{R}.


Note: 00 0 ^ 0 is undefined.

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