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Principal root of a Complex Number

  1. Sep 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Find all the roots in rectangular coordinates, exhibit them as vertices of certain squares, and point out which is the principal root.


    3. The attempt at a solution

    The problem is [tex](-8 -8\sqrt{3}i)^{\frac{1}{4}}[/tex] and I found the four roots easily to be

    [tex]\pm(\sqrt{3} - i), \pm(1 + \sqrt{3}i)[/tex]. So when it says to exhibit them as vertices of certain squares does this mean I should just graph the four points? and it should be a square.

    Also as for which point is the principal root I have no clue. I am guessing it has something to do with principal argument but I am having trouble finding much information on principal roots.
     
  2. jcsd
  3. Sep 10, 2009 #2
    For any non-zero complex number, its fourth roots are arranged on the vertices of a square. You are being asked to verify this for the given number.

    If I'm not mistaken, the principal root is the root whose standardized argument is least.

    --Elucidus
     
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