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Representing complex number as a vector.

  1. Mar 23, 2009 #1
    180px-Complex_number_illustration.svg.png

    In the above image the default format of a complex number is taken as a vector, since vector addition is only between 2 similar units (example 10 cos 30 cm + 10 sin 30 cm or 5 cms on y axis and 2 cm on the x; which gives a resultant following vector addition), it can be said that that the real and imaginary part (taken as individual axes) are having the same units; what I mean here is that in a complex number, a + bj, a and bj are having the same units; i.e the magnitude is divided into real and imaginay parts and it gives a resultant following vector addition (a + bj).

    Infact this is the reason why they get added, cause addition of 2 numbers is only possible if the units are common.

    So if you get a complex number in physics, its (a+ib) units; it cant be a [unit 1] + ib [unit 2].


    Am I right?
     
    Last edited: Mar 23, 2009
  2. jcsd
  3. Mar 23, 2009 #2

    HallsofIvy

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    I'm not clear what you are saying. What units are you talking about? There are no "units" such as m, inches, etc. in number systems.
     
  4. Mar 23, 2009 #3
    Yes :rofl:

    But, lets take the practical application, I mean :rofl: number systems are used in physics right?...it its given a unit, when a complex number comes in a real life situation, it does have a unit, what I'm asking here is it necessary for both the real and imaginary parts to have the same unit?

    If not that image might be wrong in a few place, that's not possible considering the graphical representation of every complex number.
     
  5. Mar 23, 2009 #4

    HallsofIvy

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    Please give an actual situation in which a measured quantity, i.e. a quantity with units, is complex!
     
  6. Mar 23, 2009 #5
    ... Well, yes, if you have (a + bi), then a and bi both have the same units.

    But a, b, and i are all dimensionless. Hence, they trivially have the same dimension.
     
  7. Mar 23, 2009 #6
    Yes you are right. Don't forget that the real numbers R is a subset of the complex numbers C. The imaginary unit i is just a number which has a meaning which you know.
    The fact that 'a is a real number' also mean that 'a is a complex number'. Two vectors can be added if they are of the same dimension, since they are from the same vector space. So if you take a real number 'a' which is in it sense a complex, and add it to complex number ib, the result will give a complex number a + ib.
     
  8. Mar 23, 2009 #7
    Thank you people.

    Problem solved.
     
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