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I'm kind of in the opposite camp. If Schanuel's conjecture is true, then e^iπ = 0 would be the only non-trivial relation between e, π, and i over the complex numbers. And the fact that we already found it seems unlikely.


you mean e^(i pi)=-1, which is known as Euler's identity and is a specific case of Euler's formula

e^(i theta) = cos theta + i sin theta

That formula gives infinitely many trivial relationships like this due to the symmetry of the unit circle

e^(i 2 pi) = 1

e^(3i/2pi)/i=1

e^(5i/2pi)/i=-1

e^(i 2n pi) = 1 for all n in Z ...

etc


Thanks for ringing some bells. It's been a long time since I used that equation.




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