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Modulus Question

  1. Sep 25, 2012 #1
    1. The problem statement, all variables and given/known data
    Find all ##z=a+bi## such that:
    [tex]|z|=|z^{2}+1|[/tex]


    2. Relevant equations



    3. The attempt at a solution
    I expanded the components.
    [tex]|z|=|z^{2}+1|[/tex]
    [tex]z^{2}=a^2-b^2+2abi[/tex]
    [tex]\sqrt{a^{2}+b^{2}}=\sqrt{(a^{2}-b^{2}+1)^{2}+(2ab)^{2}}[/tex]
    [tex]a^2+b^2=(a^{2}-b^{2}+1)^{2}+(2ab)^{2}[/tex]
    [tex]0=a^{4}+2a^{2}b^{2}+b^{4}+a^{2}-3b^{2}+1[/tex]

    I don't see what to do now...
     
    Last edited: Sep 25, 2012
  2. jcsd
  3. Sep 25, 2012 #2

    jbunniii

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    That should be [itex]-b^2[/itex], not [itex]+b^2[/itex].
     
  4. Sep 25, 2012 #3
    Right. Let me just go fix that.

    Edit. Fixed
     
  5. Sep 25, 2012 #4

    jbunniii

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    Well, you fixed it in the first line where it appeared, but you still need to fix it everywhere else.
     
  6. Sep 25, 2012 #5
    I fixed then end before, I just forgot to change the middle parts.
     
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