|i|=-3.59095×10^82

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I was thinking about math, and i define the semi-algebric representation of |x|

|x|=Pi/2 + Sum[-2 (1/(E^((n 2 + 1) (I x)) ((n 2 + 1)^2 Pi))) - 2 (E^((n 2 + 1) I x)/((n 2 + 1)^2 Pi)), {n, 0, inf}]

than i apply this formula on some number and works quite well.
So, i decide to aply the imaginary number to this formula. WHAT is the |i|?

The result of |i| is -3.59095×10^82
A REAL NUMBER acording with the definition of module, but negative!!!! WHAT
and about the big number 10^82 is very very very big number for module of a imaginary number.

Can you math guys tell me what you think about this peace of math?