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Complex analysis question!

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data

    does there exist a power series that converges at z= 2+31 and diverges at z=3-i

    Im really stuck on this one! any ideas?
     
  2. jcsd
  3. Nov 22, 2009 #2

    Dick

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    Do you mean 2+3i and 3-i? And do you mean a power series centered at z=0? There is a theorem about convergence of power series based on a radius of convergence. Can you find it?
     
  4. Nov 22, 2009 #3
    Yes, sorry my question is to determine whether there exists a power series that converges at z = 2 + 3i and diverges at z = 3 - i.
     
  5. Nov 22, 2009 #4

    Dick

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    Ok, so is the power series just a sum of z^i (as opposed to (z-c)^i)? And what do you know about 'radius of convergence'?
     
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