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Complex Vectors expression

  1. Jul 12, 2009 #1
    Problem/Statement
    The complex vector, [tex]\hat{v}(t) = cos(\omega t)\hat{x} + sin(\omega t)\hat{y}[/tex] is the unit vector [tex]\hat{v}(t)[/tex] expressed in instantaneous form.

    Question
    What I am wondering is, why is there no imaginary component "j" in say the sin component for the equation above?

    Can we express a general notation for complex vectors as,
    [tex]\hat{v}(t) = [cos(\omega t) + sin(\omega t)]\hat{x}] + [cos(\omega t) + sin(\omega t)]\hat{y}] [/tex]? Shouldn't that be the notation for the instantaneous form also?


    Thanks,


    Jeff
     
    Last edited: Jul 13, 2009
  2. jcsd
  3. Jul 13, 2009 #2
    Weird. You'd have to consult the source of the question (either your book or your professor or whatnot).

    With the hats over the x and y, it almost looks like they are mixing R^2 and C. The two are, in fact, isomorphic, and anything you can say about complex numbers translates simply to a statement about vectors in a 2D plane.

    If it were me, I'd make the assumption that they meant x = 1 and y = j. That way, v(t) is a complex number. (In fact, v would be the exponential function, [tex]e^{it}[/tex]).
     
  4. Jul 13, 2009 #3
    Yea, I'm not sure. I think I will ask the teacher tomorrow. Oh I think I meant the following (as well),

    Can we express a general notation for complex vectors as,
    [tex]\hat{v}(t) = [[cos(\omega t) + sin(\omega t)]\hat{x} + j[cos(\omega t) + sin(\omega t)]\hat{y}] [/tex]? Shouldn't that be the notation for the instantaneous form also?
     
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