Does a power series converge at z=2+3i and diverge at z=3-i?

[mariab89]

Homework Statement

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?

 

[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?

 

[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.

 

[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'?