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Thread: Help defining i?

  1. #1 Help defining i? 
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    I have recently committed myself to comprehending complex numbers. In trying to find a place to start that succinctly defines the nature of numbers, I feel the best place to start is with understanding the construction to i, or, the square root of -1.


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    No idea where to start with it....


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    Forum Radioactive Isotope MagiMaster's Avatar
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    is the start. Everything else follows from that.
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    is just another way of writing
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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    Quote Originally Posted by Arcane_Mathematician View Post
    is just another way of writing
    this much I comfortably comprehend. It is the solution that i represents that I am trying to grasp.
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    Quote Originally Posted by Re-strained View Post
    Quote Originally Posted by Arcane_Mathematician View Post
    is just another way of writing
    this much I comfortably comprehend. It is the solution that i represents that I am trying to grasp.
    To provide this with further definition, as far as real numbers go, it is my thought that i describes a contour that provides zero not as an absence of information, but as the equilibrium of information. This is the reason I have chosen to start here in studying complex numbers......
    Last edited by Re-strained; December 23rd, 2013 at 02:15 AM.
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    KJW
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    Quote Originally Posted by Re-strained View Post
    It is the solution that i represents that I am trying to grasp.
    Don't think that way. is your starting point. All else follows from that and the rules of arithmetic.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    Quote Originally Posted by Re-strained View Post
    It is the solution that i represents that I am trying to grasp.
    Don't think that way. is your starting point. All else follows from that and the rules of arithmetic.
    OK. Will go from there. Thanks for setting me up for a challenge. I hope my answer matches your own.
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    Quote Originally Posted by Re-strained View Post
    Quote Originally Posted by Re-strained View Post
    Quote Originally Posted by Arcane_Mathematician View Post
    is just another way of writing
    this much I comfortably comprehend. It is the solution that i represents that I am trying to grasp.
    To provide this with further definition, as far as real numbers go, it is my thought that i describes a contour that provides zero not as an absence of information, but as the equilibrium of information. This is the reason I have chosen to start here in studying complex numbers......
    ie, providing i with a value identifies the equilibrium associated to 0......
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  11. #10  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by Re-strained View Post
    ie, providing i with a value identifies the equilibrium associated to 0......
    I don't know what that means. As others suggest, I would concentrate on the algebraic/arithmetic properties of i and the complex numbers.

    If you want to give it meaning, then look at the complex plane and consider multiplication by i as rotation by 90 (and multiplication by -1 as rotation by 180).
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Re-strained View Post
    ie, providing i with a value identifies the equilibrium associated to 0......
    I don't know what that means. As others suggest, I would concentrate on the algebraic/arithmetic properties of i and the complex numbers.

    If you want to give it meaning, then look at the complex plane and consider multiplication by i as rotation by 90 (and multiplication by -1 as rotation by 180).
    Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.
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    [QUOTE=Strange;506365]
    Quote Originally Posted by Re-strained View Post

    If you want to give it meaning, then look at the complex plane and consider multiplication by i as rotation by 90 (and multiplication by -1 as rotation by 180).
    That is useful information certainly. Thank you.
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    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by Re-strained View Post
    Quote Originally Posted by Re-strained View Post
    To provide this with further definition, as far as real numbers go, it is my thought that i describes a contour that provides zero not as an absence of information, but as the equilibrium of information. This is the reason I have chosen to start here in studying complex numbers......
    ie, providing i with a value identifies the equilibrium associated to 0......
    Quote Originally Posted by Re-strained View Post
    Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.
    Welcome back, 3SwordBunny.
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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    Genius Duck Moderator Dywyddyr's Avatar
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    Quote Originally Posted by Re-strained View Post
    Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.
    Oh boy...
    "[Dywyddyr] makes a grumpy bastard like me seem like a happy go lucky scamp" - PhDemon
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  16. #15  
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Re-strained View Post
    Quote Originally Posted by Re-strained View Post
    To provide this with further definition, as far as real numbers go, it is my thought that i describes a contour that provides zero not as an absence of information, but as the equilibrium of information. This is the reason I have chosen to start here in studying complex numbers......
    ie, providing i with a value identifies the equilibrium associated to 0......
    Quote Originally Posted by Re-strained View Post
    Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.
    Welcome back, 3SwordBunny.
    Thank you for helping unmuddle my question. First time in 20 years my head has not spun when I think about it. Helps...
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    Forum Freshman Durante's Avatar
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    Quote Originally Posted by Re-strained View Post
    Without identifying the equilibrium one is measuring, numbers are without real definition. If you are measuring a system, providing that systems value to i, subsequently defines the equilibrium you are measuring and 0 as that equilibrium's epicentre.
    Why are you typing like that? It makes you look silly, not smart.
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