# Complex analysis question!

1. Nov 22, 2009

### mariab89

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. Nov 22, 2009

### Dick

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?

3. Nov 22, 2009

### mariab89

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.

4. Nov 22, 2009

### Dick

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'?