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.
by
Calvin Lin