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Evaluate $i^{11} + i^{16} + i^{21} + i^{28} + i^{31}$.

 Feb 21, 2021
 #1
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Powers of i cycle in groups of 4:

 

i^0 = 1

i^1 = i

i^2 = -1

i^3 = -i

 

\(i^{11} + i^{16} + i^{21} + i^{28} + i^{31} = -i + 1 + i + 0 - i = \boxed{1-i}\)

 Feb 21, 2021

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