Comment by qnleigh
5 hours ago
Uuuuuum no?
e^(ix) = cos(x) + isin(x). In particular e^(ipi) = -1
(1 + 1/n)^n = e. This is part of what makes e such a uniquely useful exponent base.
Not applied enough? What about:
d/dx e^x = e^x. This makes e show up in the solutions of all kinds of differential equations, which are used in physics, engineering, chemistry...
The Fourier transform is defined as integral e^(iomega*t) f(t) dt.
And you can't just get rid of e by changing base, because you would have to use log base e to do so.
Edit: how do you escape equations here? Lots of the text in my comment is getting formatted as italics.
Guessing the original comment hasn't taken complex analysis or has some other oriented view point into geometry that gives them satisfaction but these expressions are one of the most incredible and useful tools in all of mathematics (IMO). Hadn't seen another comment reinforcing this so thank you for dropping these.
Cauchy path integration feels like a cheat code once you fully imbibe it.
Got me through many problems that involves seemingly impossible to memorize identities and re-derivation of complex relations become essentially trivial
> Edit: how do you escape equations here? Lots of the text in my comment is getting formatted as italics.
Just escape any asterisks in your post that you want rendered as asterisks: this: \* gives: *.