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Find all solutions to Log(z^3-9)=(pi)*i ,z = a +bi

  1. Mar 30, 2009 #1
    1. The problem statement, all variables and given/known data

    Sorry to repost this but no one replied to my other thread.

    find all solutions to Log(z^3-9)=(pi)*i ,z = a +bi

    3. The attempt at a solution

    z^3-9 = e^(pi*i)

    e^(pi*i)=-1

    z^3 = -1 + 9

    then the problem becomes finding the roots of

    z^3 = 8

    which are -1 - sqrt(3)i, -1 + sqrt(3)i, and 2

    did I get this right? Thanks.
     
  2. jcsd
  3. Mar 30, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, that is correct.
     
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