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Filled Julia set - check my solution if it is right.

  1. Feb 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose f(z) = z^3 -27z + 15
    Find R such that |f(z)|>|z| whenever |z|>R.

    2. Relevant equations



    3. The attempt at a solution
    Let f(z)=z, then I have z^3 -28z + 15 = 0
    then,

    z=5, (-5+√(17))/2, (-5-√(17))/2.

    since 5 is the most further point, R=5.

    check my solution if it is right. I did it, but im not so sure.
     
  2. jcsd
  3. Feb 3, 2012 #2

    lanedance

    User Avatar
    Homework Helper

    so at z=5, f(5) = 0 and at z=5+e, for some small e>0, f will still be pretty small, so I don't think you've nailed it

    you need to find where
    |f(z)|-|z|>0
     
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