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.
physics
asked Dec 4 '18 at 2:47
Xavier Stanton
319211
add a comment |
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.
physics
asked Dec 4 '18 at 2:47
Xavier Stanton
319211
1
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 $j^2 = 0$.
– Eevee Trainer
Dec 4 '18 at 2:49
5
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).
– T. Bongers
Dec 4 '18 at 2:49
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
– Hugo
Dec 4 '18 at 2:50
5
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
– achille hui
Dec 4 '18 at 3:02
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
– Xavier Stanton
Dec 5 '18 at 0:54
add a comment |
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.
physics
asked Dec 4 '18 at 2:47
Xavier Stanton
319211
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.
physics
physics
asked Dec 4 '18 at 2:47
Xavier Stanton
319211
asked Dec 4 '18 at 2:47
Xavier Stanton
319211
asked Dec 4 '18 at 2:47
Xavier Stanton
319211
asked Dec 4 '18 at 2:47
Xavier Stanton
319211
asked Dec 4 '18 at 2:47
Xavier Stanton
319211
319211
1
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 $j^2 = 0$.
– Eevee Trainer
Dec 4 '18 at 2:49
5
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).
– T. Bongers
Dec 4 '18 at 2:49
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
– Hugo
Dec 4 '18 at 2:50
5
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
– achille hui
Dec 4 '18 at 3:02
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
– Xavier Stanton
Dec 5 '18 at 0:54
add a comment |
1
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 $j^2 = 0$.
– Eevee Trainer
Dec 4 '18 at 2:49
5
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).
– T. Bongers
Dec 4 '18 at 2:49
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
– Hugo
Dec 4 '18 at 2:50
5
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
– achille hui
Dec 4 '18 at 3:02
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
– Xavier Stanton
Dec 5 '18 at 0:54
1
1
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 $j^2 = 0$.
– Eevee Trainer
Dec 4 '18 at 2:49
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 $j^2 = 0$.
– Eevee Trainer
Dec 4 '18 at 2:49
5
5
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).
– T. Bongers
Dec 4 '18 at 2:49
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).
– T. Bongers
Dec 4 '18 at 2:49
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
– Hugo
Dec 4 '18 at 2:50
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
– Hugo
Dec 4 '18 at 2:50
5
5
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
– achille hui
Dec 4 '18 at 3:02
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
– achille hui
Dec 4 '18 at 3:02
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
– Xavier Stanton
Dec 5 '18 at 0:54
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
– Xavier Stanton
Dec 5 '18 at 0:54
add a comment |
1 Answer
1
active
oldest
votes
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 $j=e^{frac{2ipi}{3}}$
There probably are more notations but those are the most used and the ones I know
answered Dec 4 '18 at 9:07
TheD0ubleT
39218
add a comment |
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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 $j=e^{frac{2ipi}{3}}$
There probably are more notations but those are the most used and the ones I know
answered Dec 4 '18 at 9:07
TheD0ubleT
39218
add a comment |
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 $j=e^{frac{2ipi}{3}}$
There probably are more notations but those are the most used and the ones I know
answered Dec 4 '18 at 9:07
TheD0ubleT
39218
add a comment |
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 $j=e^{frac{2ipi}{3}}$
There probably are more notations but those are the most used and the ones I know
answered Dec 4 '18 at 9:07
TheD0ubleT
39218
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 $j=e^{frac{2ipi}{3}}$
There probably are more notations but those are the most used and the ones I know
answered Dec 4 '18 at 9:07
TheD0ubleT
39218
answered Dec 4 '18 at 9:07
TheD0ubleT
39218
answered Dec 4 '18 at 9:07
TheD0ubleT
39218
answered Dec 4 '18 at 9:07
TheD0ubleT
39218
39218
add a comment |
add a comment |
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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 $j^2 = 0$.
– Eevee Trainer
Dec 4 '18 at 2:49
5
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).
– T. Bongers
Dec 4 '18 at 2:49
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
– Hugo
Dec 4 '18 at 2:50
5
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
– achille hui
Dec 4 '18 at 3:02
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
– Xavier Stanton
Dec 5 '18 at 0:54