A math SE question asks, if α and β are transcendental, must αᵝ be transcendental also? What's the first counterexample that comes to mind? More than one Math SE person mentioned \(e^{\ln 2 }\).
But I'm amused that the first counterexample I thought of was \(e^{i\pi}\).
@mjd to me the reason I would immediately go with e^{ln 2} as the response is because it is also the example that proves that an irrational number raised to the power of another irrational number can be rational
@mathematicalsynesthesia I'm pretty sure that \( e^{i\pi}\) is also rational
@mjd correct that is my point. It answers both questions at the same time, using only real numbers. The number i \pi is not irrational
@mathematicalsynesthesia Of course the number iπ is irrational.
