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Homework Help: Complex numbers question

  1. Feb 18, 2006 #1
    Hi, I have no clue how to approach this question, was in my last years final exams.

    (z^2 + 1)^4 = 1

    Find all solutions, where z is a complex number.

    Tips please?
     
  2. jcsd
  3. Feb 18, 2006 #2

    arildno

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    First off, write [itex]1=e^{ik2\pi}[/itex]
    where k is an integer.
    Now, take the fourth root of the equation:
    [tex]z^{2}+1=e^{i\pi\frac{k}{2}}[/tex]
    For how many choices of k will the right-hand side represent DISTINCT complex numbers?
     
  4. Feb 19, 2006 #3

    quasar987

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    Supposing you have some experience solving equations of the type [itex]z^n=a[/itex] where a is complex...

    Set [itex]\zeta = z^2+1[/itex]. Then find all 4 solutions of [itex]\zeta^4 = 1[/itex]. Then go back to [itex]\zeta -1 = z^2[/itex] and for all four [itex]\zeta[/itex] found, find the 2 solutions of z associated, for a total of 8.
     
    Last edited: Feb 19, 2006
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