What is the number j?
$begingroup$
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 StantonXavier Stanton
311211
$endgroup$
add a comment |
$begingroup$
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 StantonXavier Stanton
311211
$endgroup$
1
$begingroup$
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 $j^2 = 0$.
$endgroup$
– Eevee Trainer
Dec 4 '18 at 2:49
5
$begingroup$
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).
$endgroup$
– T. Bongers
Dec 4 '18 at 2:49
$begingroup$
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
$endgroup$
– Hugo
Dec 4 '18 at 2:50
5
$begingroup$
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
$endgroup$
– achille hui
Dec 4 '18 at 3:02
$begingroup$
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
$endgroup$
– Xavier Stanton
Dec 5 '18 at 0:54
add a comment |
$begingroup$
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 StantonXavier Stanton
311211
$endgroup$
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 StantonXavier Stanton
311211
asked Dec 4 '18 at 2:47
Xavier StantonXavier Stanton
311211
asked Dec 4 '18 at 2:47
Xavier StantonXavier Stanton
311211
asked Dec 4 '18 at 2:47
Xavier StantonXavier Stanton
311211
asked Dec 4 '18 at 2:47
Xavier StantonXavier Stanton
311211
311211
1
$begingroup$
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 $j^2 = 0$.
$endgroup$
– Eevee Trainer
Dec 4 '18 at 2:49
5
$begingroup$
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).
$endgroup$
– T. Bongers
Dec 4 '18 at 2:49
$begingroup$
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
$endgroup$
– Hugo
Dec 4 '18 at 2:50
5
$begingroup$
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
$endgroup$
– achille hui
Dec 4 '18 at 3:02
$begingroup$
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
$endgroup$
– Xavier Stanton
Dec 5 '18 at 0:54
add a comment |
1
$begingroup$
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 $j^2 = 0$.
$endgroup$
– Eevee Trainer
Dec 4 '18 at 2:49
5
$begingroup$
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).
$endgroup$
– T. Bongers
Dec 4 '18 at 2:49
$begingroup$
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
$endgroup$
– Hugo
Dec 4 '18 at 2:50
5
$begingroup$
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
$endgroup$
– achille hui
Dec 4 '18 at 3:02
$begingroup$
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
$endgroup$
– Xavier Stanton
Dec 5 '18 at 0:54
1
1
$begingroup$
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 $j^2 = 0$.
$endgroup$
– Eevee Trainer
Dec 4 '18 at 2:49
$begingroup$
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 $j^2 = 0$.
$endgroup$
– Eevee Trainer
Dec 4 '18 at 2:49
5
5
$begingroup$
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).
$endgroup$
– T. Bongers
Dec 4 '18 at 2:49
$begingroup$
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).
$endgroup$
– T. Bongers
Dec 4 '18 at 2:49
$begingroup$
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
$endgroup$
– Hugo
Dec 4 '18 at 2:50
$begingroup$
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
$endgroup$
– Hugo
Dec 4 '18 at 2:50
5
5
$begingroup$
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
$endgroup$
– achille hui
Dec 4 '18 at 3:02
$begingroup$
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
$endgroup$
– achille hui
Dec 4 '18 at 3:02
$begingroup$
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
$endgroup$
– Xavier Stanton
Dec 5 '18 at 0:54
$begingroup$
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
$endgroup$
– Xavier Stanton
Dec 5 '18 at 0:54
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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 $j=e^{frac{2ipi}{3}}$
There probably are more notations but those are the most used and the ones I know
answered Dec 4 '18 at 9:07
TheD0ubleTTheD0ubleT
39218
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3025057%2fwhat-is-the-number-j%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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 $j=e^{frac{2ipi}{3}}$
There probably are more notations but those are the most used and the ones I know
answered Dec 4 '18 at 9:07
TheD0ubleTTheD0ubleT
39218
$endgroup$
add a comment |
$begingroup$
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 $j=e^{frac{2ipi}{3}}$
There probably are more notations but those are the most used and the ones I know
answered Dec 4 '18 at 9:07
TheD0ubleTTheD0ubleT
39218
$endgroup$
add a comment |
$begingroup$
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 $j=e^{frac{2ipi}{3}}$
There probably are more notations but those are the most used and the ones I know
answered Dec 4 '18 at 9:07
TheD0ubleTTheD0ubleT
39218
$endgroup$
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
TheD0ubleTTheD0ubleT
39218
answered Dec 4 '18 at 9:07
TheD0ubleTTheD0ubleT
39218
answered Dec 4 '18 at 9:07
TheD0ubleTTheD0ubleT
39218
answered Dec 4 '18 at 9:07
TheD0ubleTTheD0ubleT
39218
39218
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3025057%2fwhat-is-the-number-j%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
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 $j^2 = 0$.
$endgroup$
– Eevee Trainer
Dec 4 '18 at 2:49
5
$begingroup$
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).
$endgroup$
– T. Bongers
Dec 4 '18 at 2:49
$begingroup$
Actually we never use any alphabet to represent a rational number, although I don't really know what this is.
$endgroup$
– Hugo
Dec 4 '18 at 2:50
5
$begingroup$
If $i,j,k$ appear together, they may refer to the standard imaginary units of quaternions.
$endgroup$
– achille hui
Dec 4 '18 at 3:02
$begingroup$
Only because I've seen people say this, but I mean $j$ alone. I know about the quaternions.
$endgroup$
– Xavier Stanton
Dec 5 '18 at 0:54