Bravo Euler
Bravo Gauss
>not understanding complex analysis
Wow OP.
>>8039142
have you ever heard of modulo 2pi ?
>>8039142
[math](e^{\pi i})^2 = (-1)^2[/math]
does not follow from
[math]e^{\pi i} = -1[/math]
>>8039306
Can you point me to a number that can give you two different values when you square it?
>>8039319
Sure. Try [math]2^i[/math]. Or any number raised to the ith power.
Hint: It's the i that fucks it up
>>8039323
not this guy but
the stuff that doesn't follow up is the logarithm
>>8039332
Perhaps, but that step is also incorrect.
>>8039323
That's because [math]s^i[/math] doesn't give a single well defined number because it's defined by logarithms. On the other hand, [math]e^{2\pi i}[/math] doesn't have this issue, and you can immediately verify that [math](e^{\pi i})^2 = (-1)^2[/math]
ln 1 has many complex roots besides real solution 0
2 pi i is one of them
>>8039337
You're squaring the indices
>>8039337
That's clearly no the same that in OP. I hope you are trolling.
>>8039142
anon, you've just witnessed
SPOOKY SCARY IMAGINARY NUMBERS
>>8039337
>>8039323
[eqn]
\begin{aligned}
2^i &= e^{i \ln{2}} \\
&= \cos{(\ln{2})} + i \sin{(\ln{2})} \\
&\approx 0.76924 + 0.63896i
\end{aligned}
[/eqn] What's [math]i[/math] doing that's fuggery again?
>>8039142
He's abusing the fact that the complex plane isn't one-to-one.
If he mentions that e^0 = e^2*pi*i then this shit is trivial.
>>8039829
>He's abusing the fact that the complex plane isn't one-to-one.
the people who say shit like this are worth than the original posters
>>8039834
Do you have anything constructive add? Like, for instance, why that's "worth than the original posters"?
>that feel when complex analysis
http://www.wolframalpha.com/input/?i=ln+%28e^%28i+x%29%29
>>8039839
>complex plane isn't one-to-one.
>plane
>one-to-one
>plane
>one-to-one
also
>Do you have anything constructive add?
>constructive add?
hoisted with your own petard motherfucker
>>8039142
>OP doesnt know how the complex logarithm works
>point at him and laugh
>>8039775
Not my fault mathematicians just keep making stuff up
