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ii=(eiπ/2)i=e−π/2 i^i = \big(e^{ i \pi / 2} \big)^i = e^{- \pi / 2} ii=(eiπ/2)i=e−π/2 It is (initially) surprising that an imaginary number raised to an imaginary number results in a real number.
Characterize all positive kkk such that (ik)ik∈R. (ik)^{ik} \in \mathbb{R}. (ik)ik∈R.
Note: 00 0 ^ 0 00 is undefined.
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