Overheard at work: "[A coworker] just showed me that the cartesian coordinate (2,1) can be written as 2+1i ....mind blown"
I love it when #mathematics actually happens in the workplace (we're trying to figure out how to work with some satellite data).
@popefucker Oh, you mean like how there's an isomorphism \( f: \mathbb{C} \to \mathbb{R}^2 \) given by
\[
f(a + bi) := \begin{pmatrix}
a & -b \\
b & a
\end{pmatrix}?
\]
@popefucker Btw, that toot looks better rendered. I was hoping perhaps your instance also rendered it:
@JordiGH no, unfortunately, I'm using a mobile app, but I speak latex
@JordiGH actually most of the properties of complex functions come from that isomorphism, as the cauchy-reimmann equations pretty much fall out of it and those are the basis for most of the weirdness of complex functions
@JordiGH i have a task about every quarter that requires me to use spherical polars, now it's just code but 1st time solving it realised they were the answer was joy.
@JordiGH the day that a professor explained that complex multiplication is actually just a linear transformation was the day I truly understood complex numbers