Imaginary game

Algebra Level 2

i+i2+i3+i4+i5+i6+i7+i8++i20=?\large i+i^2+i^3+i^4+i^5+i^6+i^7+i^8+ \ldots +i^{20} = ?

Notation: i=1i = \sqrt{-1} denotes the imaginary unit.

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