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Homework Help: Complex roots

  1. Aug 18, 2006 #1
    I think I've got some minor braindamage or something but i just can't remember how to find the singular points of


    I guess the problem is to solve the equation 1+x^4=0 and get complex roots but this is what I don't remember how to do. Thanks.
  2. jcsd
  3. Aug 18, 2006 #2


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    Start off by substituting v=x2, and try to go from there
  4. Aug 18, 2006 #3


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    Or swith to an easier, but equivalent, representation of the complex number z (think exponential/polar/...)
  5. Aug 20, 2006 #4


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    Hint: $w^2+1=(w+i)(w-i)$
  6. Aug 21, 2006 #5
    Write x^4 = -1 and try to follow what you think is the simplest path without involving anything fancy.
  7. Aug 21, 2006 #6


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    Well, use the decomposition

    [tex]z^4 +1 =(z^2 +i)(z^2 -i) [/tex]

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