1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook