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For the purposes of the ACT, you should remember the pattern for imaginary numbers: i = i, i^{2} = -1, i^{3} = -i, i^{4} = 1, then the pattern continues to repeat.

Example: What is i^{23}? (Find the closest multiple of 4 that is less than 23. It is 20. i^{20}=i^{4}. Then count up to 23: i^{21}=i^{1}, i^{22}=i^{2}, and finally, i^{20}=i^{3}, which equals -i, so i^{23} = -i.

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