$\displaystyle x \in \mathbb{R}, e^{x} = e^{x \frac{2 \pi i}{2 \pi i}} = e^{2 \pi i \frac{x}{2 \pi i}} = (e^{2 \pi i})^{\frac{x}{2 \pi i}} = (cos(2 \pi) + i \text{ } sin(2 \pi))^{\frac{x}{2 \pi i}} = 1 $

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- Sep 7th 2013, 10:05 PMLord VoldemortFind the error!
$\displaystyle x \in \mathbb{R}, e^{x} = e^{x \frac{2 \pi i}{2 \pi i}} = e^{2 \pi i \frac{x}{2 \pi i}} = (e^{2 \pi i})^{\frac{x}{2 \pi i}} = (cos(2 \pi) + i \text{ } sin(2 \pi))^{\frac{x}{2 \pi i}} = 1 $

- Sep 8th 2013, 02:15 AMShakarriRe: Find the error!
I think the error is in the step $\displaystyle e^{x\frac{2i\pi}{2i\pi}}=e^{2i\pi\frac{x}{2i\pi}$ For similar reasons to why this is incorrect:

$\displaystyle e^{i\pi}=-1$

$\displaystyle e^{2i\pi}=1$

$\displaystyle ln(e^{2i\pi})=ln(1)$

$\displaystyle 2i\pi=0$ - Sep 8th 2013, 04:37 AMtopsquarkRe: Find the error!
- Sep 8th 2013, 06:39 AMLord VoldemortRe: Find the error!
- Sep 8th 2013, 06:53 AMtopsquarkRe: Find the error!
- Apr 23rd 2014, 01:46 PMfu456789Re: Find the error!
Greetings mathematicians,

On a much lighter note -

The error is here:

Attachment 30753

XD

fu456789