# justifying convergence of complex series

The question asks me to justify if the complex series converges absolutely, which leads me to think that I should use the comparison test (instead of the root or ratio tests), the series itself is sum from n=1 to infinity of $$1/(n^2+i)$$ But I'm not sure how to find another series to compare it to now that it is complex? Thanks!

Hint: $$|n^2+i|\geq|n^2|-|i|= n^2-1 .$$
• If $a\ge b$ then $1/a\le 1/b$. – Julián Aguirre Oct 9 '16 at 18:27
• Actually $|n^2+i| > n^2.$ – zhw. Oct 10 '16 at 17:34