Everything Can Be Cancelled Off?

Algebra Level 3

i+i2+i3+i4++in=1 \large i + i^2 + i^3 + i^4 + \cdots + i^n = - 1

The equation above holds true for some positive integer nn. Which of the following is a possible value of nn?

Clarification: i=1i=\sqrt{-1}.

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