# Imaginary^Imaginary

Algebra Level 4

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

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

Note: $$0 ^ 0$$ is undefined.

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