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Difference between i and j?

  1. Jun 26, 2013 #1
    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. jcsd
  3. Jun 26, 2013 #2
    Where exactly did you hear this?
     
  4. Jun 26, 2013 #3

    mathman

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    Mathematicians and physicists:√-1 = i
    Electrical engineers: √-1 = j (they use i for current)
     
  5. Jun 26, 2013 #4
    this is where i heard it
     
    Last edited by a moderator: Sep 25, 2014
  6. Jun 26, 2013 #5

    Mark44

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    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.
     
  7. Jun 26, 2013 #6
    okay thanks, i guess the video was wrong
     
  8. Jun 26, 2013 #7

    Mark44

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    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.
     
  9. Jun 27, 2013 #8

    HallsofIvy

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    One of the wonderful things about the internet is that even idiots can post!
     
  10. Jun 29, 2013 #9
    *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
  11. Jun 29, 2013 #10

    pwsnafu

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    You do realize that the split-complex numbers are a thing in mathematics, right?
     
  12. Jun 29, 2013 #11
    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.
     
  13. Jun 29, 2013 #12
    confusion?

    Do you mean j2=1 or -1

    Or do you mean the axises i^.j^,^k
     
  14. Jun 30, 2013 #13

    D H

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    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 [itex]\hat{\imath}[/itex], [itex]\hat{\jmath}[/itex], and [itex]\hat{k}[/itex] to indicate the unit vectors in three space comes directly from the quaternions.
     
  15. Jun 30, 2013 #14

    robphy

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    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.
     
  16. Jan 1, 2015 #15
    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?
     
  17. Jan 1, 2015 #16
    then what about the current density for which we use the same notation j?
     
  18. Jan 1, 2015 #17

    FactChecker

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    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.
     
  19. Jan 1, 2015 #18

    HallsofIvy

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    The difference between 'i' and 'j' is the difference between normal people and electrical engineers!
     
  20. Jan 1, 2015 #19

    jasonRF

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    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 [itex]e^{j \omega t}[/itex] time dependence, and i for [itex]e^{-i \omega t}[/itex]. The mapping between results is then straightforward.
     
  21. Jan 1, 2015 #20
    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?
     
  22. Jan 1, 2015 #21

    FactChecker

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    Maybe 'i' came from the math side where 'imaginary' roots had to be explained. Leibniz called them "impossible" numbers.
     
  23. Jan 1, 2015 #22

    jedishrfu

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  24. Jan 2, 2015 #23

    jasonRF

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    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
     
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