i¹⁰¹ + i¹⁰² + i¹⁰³ + i¹⁰⁴ = ____?
- -i
- 1
- 0
- None of these
Explanation
To find the sum, we need to calculate each term:
i^101 = i (since i^1 = i and the powers repeat every 4 terms)
i^102 = i^2 = -1
i^103 = i^3 = -i
i^104 = i^4 = 1
Now, let's add them up:
i + (-1) + (-i) + 1 = 0
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