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I've found an exact equation for e without pi

e=(cos(1/2)+i*sin(1/2))^(2/i)

does this mean that e is not a transcendental number?

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does this mean that e is not a transcendental number?

No, we have proofs that e is transcendental. Having a closed expression that like, which is correct, does not change these proofs.

##### Share on other sites You are pretty much just isolating e from the equation.

##### Share on other sites You are pretty much just isolating e from the equation.

You're pretty ,much right - but the above is a bit of a over-complicated

cosx+isinx = e^ix

cos1/2+isin1/2 = e^(i/2)

(e^(i/2))^(2/i)=e

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I've found an exact equation for e without pi

e=(cos(1/2)+i*sin(1/2))^(2/i)

does this mean that e is not a transcendental number?

If you find a polynomial with rational coefficients that has e as a zero, then e would not be transcendental. That's the definition.

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Herein the definition of transcendental number....

en.wikipedia.org/wiki/Transcendental_number

Now u know the definition... So, your formula doesn't proof whether it is transcendent or not.

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