complex jw vector

Discussion in 'Math' started by TheSpArK505, Dec 12, 2014.

  1. TheSpArK505

    Thread Starter Member

    Sep 25, 2013
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    0
    Hello guys.
    I have a complex vector that starts at a+(jw)b and terminates at c+(jw)d

    do i calculate the length and angle as following or do Complex vectors have their own special formulas

    length=sqrt[(c-a)^2+(d-b)^2]

    angle= arctan[(d-b)/(c-a)]
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,143
    1,790
    Not quite. You need to account for ω in your calculations.

    L = \sqrt{(c-a)^2+(d\omega-b\omega)^2}

    \angle=\arctan(\frac{d\omega-b\omega}{c-a})
     
  3. TheSpArK505

    Thread Starter Member

    Sep 25, 2013
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    but w is not given
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,143
    1,790
    Then you cannot calculate a specific length. You can only say that length is a function of ω, or give the length for several values of ω. If ω=1 then your original formulation is correct. In which case you might want to rethink your original question. Does that help you?
     
  5. TheSpArK505

    Thread Starter Member

    Sep 25, 2013
    92
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    OK here the problem attached
     
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  6. TheSpArK505

    Thread Starter Member

    Sep 25, 2013
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  7. Papabravo

    Expert

    Feb 24, 2006
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    Right, I have the same book. I see an ω as a label for the imaginary axis,but that ω is not used in the evaluation of points in the complex plane. A general point is expressed as

    a + jb, or c+jd​

    and your original answer is correct.
     
  8. TheSpArK505

    Thread Starter Member

    Sep 25, 2013
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    OK but for the angle when s=-3+j4
    I calculated the angle as theta =arctan[(4-0)/(-3-(-1))] i got -63.43 degree . how come???
    @Papabravo
     
  9. Papabravo

    Expert

    Feb 24, 2006
    10,143
    1,790
    The domain of the arctangent function is [-∞,+∞]
    The range of the arctangent function is [-90°,+90°]
    To get the postive angle you seek you need to add 180° to your result

    -63.43° + 180° ≈ 116.6°​

    Another way to look at it is that -63.43° is the angle from -3+j4 to the zero at -1+j0, while 116.6° is the angle from the zero at -1+j0 to the point a -3+j4
    Does that clear things up?
     
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