Cool solution

Calculus Level 4

The series

\[\sum_{z \in \mathbb{Z}[i] \setminus \{ 0 \}} \frac{1}{|z|^2}\]

is?

Note: \(\mathbb{Z}[i]\) is the set of all gaussian integers; that is, numbers of the form \(a+ib\) where a and b are integers.

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