I have this question, it asks to find the set of C numbers (z) where the series below converges.

http://img705.imageshack.us/img705/5764/unledsi.th.jpg

What I've done so far is found the series by trial and error then taken the absolute value and found that it converges for (x^2 +y^2)<2 so the set is a circle of radius 2, but I'm not sure if that is correct.

I've tried doing the ratio test on the series but it got ugly, so I split it into two series and found (z/2)<1 and 2z<1 which is close to the mod of what I got before.

Is this the right way to do it?

Thanks, Daniel