I need help with the following:

= ?

Thanks

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- December 1st 2009, 09:50 AMrainerantiderivative involving euler's formula
I need help with the following:

= ?

Thanks - December 1st 2009, 12:47 PMAryth

<--- Euler's Formula

<--- Euler's Formula for -x

- December 1st 2009, 01:57 PMDrexel28
- December 1st 2009, 03:38 PMrainer
But wait, so you guys are saying that

?

and that, since the antiderivative of e^x is e^x,

?

That would contradict

wouldn't it? - December 1st 2009, 03:47 PMDefunkt
- December 2nd 2009, 06:40 AMrainer

Okay sorry. I spazzed out there for a second. Now I got it.

But while we're on the subject, the wikipedia page on i does say that i= -i.

If that is true, then wouldn't it follow that:

?

The wikipedia quote Verbatim:

"If all mathematical textbooks and published literature referring to imaginary or complex numbers were rewritten with −*i*replacing every occurrence of +*i*(and therefore every occurrence of −*i*replaced by −(−*i*) = +*i*), all facts and theorems would continue to be equivalently valid" - December 2nd 2009, 06:41 AMDrexel28
- December 2nd 2009, 06:54 AMrainer
Say what?

- December 2nd 2009, 06:57 AMDrexel28
Basically the concept is that arose from solving . But the FTA tells us that there must be two solutions, obviously . As a convention then we take (sort of). We could have, with equal validity, make the convention that in which case everything would be different. But this is no way means that