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Argument of complex number

  1. Jul 25, 2014 #1
    1. The problem statement, all variables and given/known data
    Calculate argument of complex number
    [tex]-1-\sqrt{3}i[/tex]

    2. Relevant equations

    3. The attempt at a solution
    The argument of this is -120 degrees but why couldn't we aswell say it's 240 degrees? Since going 240 degrees will go to the same point as -120 degrees. Why is this false?
     
  2. jcsd
  3. Jul 25, 2014 #2

    HallsofIvy

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    Why do you say it is false? Yes, -120 degrees is the same as 360- 120= 240. If your text book gives -120 as the argument that does not necessarily mean 240 is not. But perhaps your text is using a particular convention here: in order to avoid ambiguity some texts require that angles be given between -180 and 180 degrees, others between 0 and 360 degrees.

    (Personally, I would have said that the argument was [itex]4\pi/3[/itex]. I am a little surprised you are using degrees rather than radians.)
     
  4. Jul 25, 2014 #3

    Mentallic

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    The answer can be any multiple of [itex]2\pi[/itex] radians, but it's just been chosen so that the principal argument (smallest angle) is in the range [itex](-\pi,\pi][/itex]. It's just a custom really.
     
  5. Jul 25, 2014 #4
  6. Jul 25, 2014 #5

    Mentallic

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    Wolfram Alpha is abiding by the principal argument custom. When you use calculators, you sometimes need to have an understanding of what their unexpected results could mean.

    Like this one:

    http://www.wolframalpha.com/input/?i=%28-1%29%5E%281%2F3%29

    Notice it says "Assuming the principal root". There are 3 roots, and the one with the smallest argument which is was returned to the user, while many people would expect the answer to be -1.
     
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