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?

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.

 

You are pretty much just isolating e from the equation.

 

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

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.

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.