Difference between i and j?

1. Jun 26, 2013

cmcraes

I know that i is the square-root of -1 but I heard that J^2=1
I was wondering what J is, why it isn't equal to one and what its used for, thanks!

2. Jun 26, 2013

micromass

Where exactly did you hear this?

3. Jun 26, 2013

mathman

Mathematicians and physicists:√-1 = i
Electrical engineers: √-1 = j (they use i for current)

4. Jun 26, 2013

cmcraes

this is where i heard it

Last edited by a moderator: Sep 25, 2014
5. Jun 26, 2013

Staff: Mentor

No, j2 = -1.
In the context of this thread, i and j are the same thing, the imaginary unit. As you already mentioned, engineers use j because they already use i for current.

6. Jun 26, 2013

cmcraes

okay thanks, i guess the video was wrong

7. Jun 26, 2013

Staff: Mentor

Yeah, the guy definitely said j2 = 1, but j ≠ 1 (which leaves the only other possibility, which is that j = -1). So he didn't know what he was talking about.

8. Jun 27, 2013

HallsofIvy

One of the wonderful things about the internet is that even idiots can post!

9. Jun 29, 2013

*This is wrong, read lower, j can be expressed as a split complex number that has mathematical importance

So j is confusing because it's also used by physicists because they use I for current. But Henry and Vi from MinutePhysics and ViHart respectively aren't wrong in their appreciation of the number j. j is not a conventional whole number or complex number, and in fact it has no mathematical relevance. To a budding mathematician, j is a simple thought experiment, or perhaps better stated, an inspiration. In the same way that i was regarded as nonsensical because root(-1) should have no solution but in the end has had huge importance in higher level mathematics and physics, j is a prompt to remember that there is more math, more math languages, more operations to be discovered/created. Its a reminder to be unconventional. j^2=1 but j is not 1. Its just an example to think beyond.

Last edited: Jun 29, 2013
10. Jun 29, 2013

pwsnafu

You do realize that the split-complex numbers are a thing in mathematics, right?

11. Jun 29, 2013

Split complex numbers- okay, maybe I was wrong. When I tried to dig up info on j=root(1) and j=/1, I didn't get anywhere. Thanks for giving me a name to look for.

12. Jun 29, 2013

utkarshraj

confusion?

Do you mean j2=1 or -1

Or do you mean the axises i^.j^,^k

13. Jun 30, 2013

D H

Staff Emeritus
It's j2, not j2, and j here refers to the hyperbolic or split-complex numbers. See the link provided by pwsnafu in post #10. The hyperbolic j is a quantity that is independent of 1 but whose square is 1. Note that -1 is not independent of 1.

Perhaps the easiest way to envision what this hyperbolic j is is to look to the quaternions. Here there are three independent quantities, i, j, and k, each of which when squared yields -1. These i, j, and k certainly doesn't make sense with normal algebra, any more than does the hyperbolic j. How can there be more than two different numbers that squared yield -1 or 1 (or for that matter, any specific number)? The solution is simple: You're not in Kansas anymore. The quaternions have their own algebra, as do the hyperbolic numbers.

The use of $\hat{\imath}$, $\hat{\jmath}$, and $\hat{k}$ to indicate the unit vectors in three space comes directly from the quaternions.

14. Jun 30, 2013

robphy

In the physics literature, they were [re]discovered as the "perplex numbers".
They provide a route to the geometry of special relativity,
just as complex numbers provides a route to Euclidean Geometry.

15. Jan 1, 2015

siva shankar

as u people said if i used by mathematicians& physicists and j only used by electronic engineers..what you suggest about the term j which is used in physics also(for same usage) ? and why are you saying like j is only for the representation of -1 ,current density also we represent with the same notation,what you mean by it?

16. Jan 1, 2015

siva shankar

then what about the current density for which we use the same notation j?

17. Jan 1, 2015

FactChecker

I just followed your link. I had never heard of this before. In split complex numbers j2 = 1. So maybe that is the context where the original post came from.

18. Jan 1, 2015

HallsofIvy

The difference between 'i' and 'j' is the difference between normal people and electrical engineers!

19. Jan 1, 2015

jasonRF

Ha Ha!

Actually, some of us EEs do use i and j interchangeably. In some instances, especially when reconciling results from physics and EE literature, it is convenient to use j for $e^{j \omega t}$ time dependence, and i for $e^{-i \omega t}$. The mapping between results is then straightforward.

20. Jan 1, 2015

The argument that EEs use $j$ instead of $i$ because $i$ is used for current has always confused me. Don't physicists come across electric current a lot as well?

21. Jan 1, 2015

FactChecker

Maybe 'i' came from the math side where 'imaginary' roots had to be explained. Leibniz called them "impossible" numbers.

22. Jan 1, 2015

Staff: Mentor

23. Jan 2, 2015

jasonRF

It is my understanding that the used of complex numbers by electrrical engineers mostly traces back to Steinmetz, who published a paper in 1893 and a few years later a textbook on AC circuit analysis. Steinmetz used j, but didn't say why (at least in my skimming of his paper). EDIT: This is pretty far off-topic from the OP - sorry!

jason