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Complex root

  1. Sep 13, 2006 #1
    I just bombed a quiz because it was 2 questions and this was one of them:

    Find all three complex roots of the following equation (give answers in polar and rectangular form)


    Looks easy enough,

    [tex] z=2e^{-i\frac{\theta}{3}} [/tex]

    This is where I think I completely realized I wasn't sure what I was doing. My roommate suggested I look for the roots of unity which I know that:


    so if I want to consider mine it should be:

    [tex]8^{1/3}(cos(\frac{\theta}{3})+isin(\frac{\theta}{3})=-8 [/tex]

    so then


    is this the right track?
    Last edited: Sep 13, 2006
  2. jcsd
  3. Sep 13, 2006 #2


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    Homework Helper

    I'm not sure what you're trying to do (eg, your second to last latex line doesn't look right). Just keep in mind that there will be a unique solution for r, and then you're left with finding the cube roots of -1 (not 1). If it helps, these are the sixth roots of 1 that aren't also cube roots of 1.
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