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Complex roots

  1. Sep 10, 2016 #1
    1. The problem statement, all variables and given/known data
    I'm looking for an explanation to something. I've attached a picture of the solution wolfram alpha is giving me.
    I understand the first two zeros, +- (-1)^(1/4)*sqrt(2).
    But i don't understand the other two zeros with the 3/4 power. Where does that power come from?
    image.png

    This isn't homework but it is course work. I thought I try some of the other problems out before diving into the actual homework and I'm already stuck lol.

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Sep 10, 2016 #2

    fresh_42

    Staff: Mentor

    Just a few questions: Why don't you supply the link to Wolfram instead? This would definitely result in a better resolution.
    Anyway, have you tried to factorize ##x^4 + 4## or to put it another way: what do you know about the roots of unity?
     
  4. Sep 10, 2016 #3

    Mark44

    Staff: Mentor

    The wolfram page mentions that these roots are multiples of the four fourth roots of unity (1). The fourth roots of 1 are i, -1, -1, and 1. They are equally spaced around the unit circle.
     
  5. Sep 10, 2016 #4
    Sorry. I'm on my phone and took a quick screen shot.
    I haven't tried to factorize it yet. I'll give that a shot. I know there is some symmetry in factoring problems like that.
    I don't know anything about roots of unity.
    I figured there was some relation between the first two solutions being 1/4 power and the other two being 3/4 power. I'm assuming "roots of unity" plays a part there.
     
  6. Sep 10, 2016 #5
    Thanks guys. The book has two pages on roots of unity that help with this problem.
     
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