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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.

Xavier Stanton
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    I've also seen $j$ used as the constant for the dual number system. It's analogous to the complex number system's $i$ constant: just that $j^2 = 0$. – PrincessEev Dec 04 '18 at 02:49
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    It's just another notation for $i$, more frequently used in engineering (also, you could have answered this pretty quickly with a Google search; rather than asking so many random questions, maybe spend some time trying to seek out resources). –  Dec 04 '18 at 02:49
  • Actually we never use any alphabet to represent a rational number, although I don't really know what this is. – Hugo Dec 04 '18 at 02:50
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    If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions. – achille hui Dec 04 '18 at 03:02
  • Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions. – Xavier Stanton Dec 05 '18 at 00:54

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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

TheD0ubleT
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