e^(pi*i)+1=0

an-salad

I have no idea what it means, (and I’m pretty sure no one else does, either) but it is the most profound thing that I have ever seen in my life.

jgill

Euler's Formula: 1740 Considering the complex plane a vector space helps to see the connections.

$e^{i x} = \cos x + i \sin x,$

javi2541997

↪jgill

Have you ever applied that mathematical formula to something?

Is it intended to be used for research purposes?

jgill

Is it intended to be used for research purposes? — javi2541997

It's useful in physics for wave functions that might otherwise be cluttered with sines and cosines. It crops up from time to time in things that interest me. For example, the DE that defines a particular contour

$\frac{dz}{dt}=iz$ , solving for $z(t)$ where $t:0\to 1$

Then
$z(t)={{z}_{0}}{{e}^{it}}$
${{z}_{0}}{{e}^{it}}={{z}_{0}}\left( \cos t+i\sin t \right)=\left( {{x}_{0}}\cos t-{{y}_{0}}\sin t \right)+i\left( {{y}_{0}}\cos t+{{x}_{0}}\sin t \right)$

e^(pi*i)+1=0

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