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: $$ |n^2+i|\geq|n^2|-|i|= n^2-1 . $$

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  • $\begingroup$ But in order to prove convergence don't I need to find something larger than the series? $\endgroup$ – Agnes Oct 9 '16 at 18:16
  • $\begingroup$ If $a\ge b$ then $1/a\le 1/b$. $\endgroup$ – Julián Aguirre Oct 9 '16 at 18:27
  • $\begingroup$ Actually $|n^2+i| > n^2.$ $\endgroup$ – zhw. Oct 10 '16 at 17:34

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