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Homework Help: Solving a polynomial equation

  1. Jan 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Happy New Year, everybody!

    Problem: Solve (z^4)+1 = 0

    2. Relevant equations

    3. The attempt at a solution

    Attempt: (z^4)+1 = 0
    ((z^2)+i)*((z^2)-i) = 0

    Could anyone help me to complete this question please?

    Many Thanks!
  2. jcsd
  3. Jan 5, 2009 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    HINT: Let [itex]z = e^{i\theta}[/itex]
  4. Jan 5, 2009 #3


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    Science Advisor

    So you know that z^2+ i= 0 and z^2- i= 0. Now you need to solve z^2= i and z^2= -i.

    You can, as Hootenanny suggested, write i and -i in "polar form" and use the fact that
    [tex]\left(re^{i\theta}\right)^{1/2}= r^{1/2} e^{i\theta/2}[/tex]
  5. Jan 5, 2009 #4

    Thanks a lot for your help HallsofIvy. I think I can do it now, thank you!
  6. Jan 5, 2009 #5

    Thanks for the hint!
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