What is the Role of J in Complex Numbers and its Use in Electrical Engineering?

[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!

 

[micromass]

Where exactly did you hear this?

 

[mathman]

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!

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

 

[cmcraes]

this is where i heard it

 

[Mark44]

I know that i is the square-root of -1 but I heard that J^2=1

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.

I was wondering what J is, why it isn't equal to one and what its used for, thanks!

 

[cmcraes]

okay thanks, i guess the video was wrong

 

[Mark44]

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.

 

[HallsofIvy]

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

 

[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.

 

[pwsnafu]

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.

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

 

[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.

 

[utkarshraj]

confusion?

Do you mean j₂=1 or -1

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

 

[D H]

Do you mean j₂=1 or -1

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.

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

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

 

[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.

 

[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?

 

[siva shankar]

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

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

 

[FactChecker]

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

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.

 

[HallsofIvy]

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

 

[jasonRF]

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

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.

 

[PFuser1232]

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?

 

[FactChecker]

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?

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

 

[jedishrfu]

In physics, we use capital I to represent current so that prevents some confusion.

Anyway, there's another proposed reason since we represent vectors in the XY plane as ai +bj and so using j to represent j^2=-1 makes sense:

http://www.johndcook.com/blog/2013/04/23/why-j-for-imaginary-unit/

and

http://en.wikipedia.org/wiki/Imaginary_unit

 

[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