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

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