I know that $$\sqrt{e^\pi}=\sqrt[i]{i}$$ which is quite a nice result, and that it is transcendental. Does the constant $e^\pi$ have any other significance? Thanks. I realize this is quite a trivial question, but I'm just curious.
2026-03-29 17:43:15.1774806195
Significance of $e^\pi$
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The expression $\sqrt[i]{i}$ is in most contexts meaningless. Even the square root of a complex number is generally ill-defined, let alone complex roots. To see the issue, consider that I could also write $e^{3 \pi} = e^{\frac{ 3 \pi i}{i}} = \sqrt[i]{e^{3 \pi i}} = \sqrt[i]{i}$.