Interesting dilemma (1 Viewer)

[deswa1]

Hey guys,

I was just looking at Euler's formula and came up with this:

<a href="http://www.codecogs.com/eqnedit.php?latex=e^{i\pi}=-1\\ e^{2i\pi}=1\textup{ (On squaring)}\\ e^{2i\pi}=e^0\\ 2i\pi=0\textup{ (On equating powers)}\\ \therefore i\pi=0" target="_blank"><img src="http://latex.codecogs.com/gif.latex?e^{i\pi}=-1\\ e^{2i\pi}=1\textup{ (On squaring)}\\ e^{2i\pi}=e^0\\ 2i\pi=0\textup{ (On equating powers)}\\ \therefore i\pi=0" title="e^{i\pi}=-1\\ e^{2i\pi}=1\textup{ (On squaring)}\\ e^{2i\pi}=e^0\\ 2i\pi=0\textup{ (On equating powers)}\\ \therefore i\pi=0" /></a>

Obviously it is wrong somewhere but I don't know where. I'm assuming the error is between the third and fourth lines but is there a reason why I can't equate powers?

Thanks

 

[Carrotsticks]

Hey guys,

I was just looking at Euler's formula and came up with this:



Obviously it is wrong somewhere but I don't know where. I'm assuming the error is between the third and fourth lines but is there a reason why I can't equate powers?

Thanks

Because the exponential definition is periodic, so you can't actually just use 0 and should use so you should have:



The equivalent of what you just said was: