e^(ix) = cos x + i sin x.
It unifies algebra, trigonometry, complex numbers, and calculus. Euler's identity is only a special case of Euler's formula, i.e., Euler's formula with x = π gives us Euler's identity: e^(iπ) = -1.
This is cute but Euler's formula is truly beautiful. In fact with x = τ = 2π, we get another cute result: e^(iτ) = 1.
From Chapter 22 of The Feynman Lectures on Physics, Volume I:"We summarize with this, the most remarkable formula in mathematics: e^(iθ) = cos θ + i sin θ. This is our jewel. We may relate the geometry to the algebra by representing complex numbers in a plane; the horizontal position of a point is x, the vertical position of a point is y. We represent every complex number, x + iy. Then if the radial distance to this point is called r and the angle is called θ, the algebraic law is that x + iy is written in the form re^(iθ), where the geometrical relationships between x, y, r, and θ are as shown. This, then, is the unification of algebra and geometry."
See the bottom of the page at https://www.feynmanlectures.caltech.edu/I_22.html for the above excerpt.
> e^(ix) = cos x + i sin x.
And that right there, is the mathematical basis for a quadrature mixer... And all of software defined radios.
https://hackaday.com/2017/05/16/if-the-i-and-q-of-software-d...
Re Bookface: https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...
Re YC founder usernames- it can't be secret if it's in the FAQ, right? https://news.ycombinator.com/newsfaq.html#yc.
None of these things are secret and to the extent you or anyone is curious about them, all you need to do is ask.
that's what I think of you.