# 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

Staff Emeritus
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

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

9. Jun 29, 2013

### CarsonAdams

*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

### CarsonAdams

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

Staff Emeritus
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

### MohammedRady

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?

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