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Homework Help: Complex Variables (Finding complex roots)

  1. Feb 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Find all solutions to (z2+1)2=-1


    3. The attempt at a solution
    I know that because it is a polynomial of degree 4 it is a square inscribed inside of a circle in the complex plane. All i really need is one solution and from that finding the other three is easy. I have tried factoring it numerous ways. the best I get it to is

    z2= i -1

    thank you!
     
  2. jcsd
  3. Feb 11, 2012 #2

    LCKurtz

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    Don't you get ##z^2=-1\pm i##? Do you know how to find the square roots of a complex number? That would give you your four roots.
     
  4. Feb 11, 2012 #3
    wow i completely left of the ± that is my problem! Let me work it and ill report back, thank you!
     
  5. Feb 11, 2012 #4
    got it,

    ±21/4*exp(i3[itex]\pi[/itex]/8)
    21/4*exp(i5[itex]\pi[/itex]/8)

    thank you again
     
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