What is the number j?
So, I've been hearing that $e$ and $i$ are not the only numbers out there that are represented and known by a single letter in the English alphabet. Apparently, there is also the number $j$. What is the number $j$ and is it irrational or not? I know it has to do with physics, but that's about it.
$\endgroup$ 51 Answer
$\begingroup$As stated in the comments $j$ is somtimes used as a substitute for $i$, usually in physics where the letter $i$ is already used ($i$ the intensity of a current for example)
It can also be used as a standard imaginary unit of quaternions. Complex numbers have $i^2 = -1$ and the quaternions have $i^2=j^2=k^2=ijk=-1$
Lastly $j$ can also represent a complex number such that $j^2+j+1=0$, or $j=e^{\frac{2i\pi}{3}}$
There probably are more notations but those are the most used and the ones I know
$\endgroup$
