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To simplify (i^{63}), we can use the fact that the powers of (i) (the imaginary unit) repeat every four cycles: (i^1 = i), (i^2 = -1), (i^3 = -i), and (i^4 = 1). To find (i^{63}), we can calculate (63 \mod 4), which gives us a remainder of 3. Therefore, (i^{63} = i^3 = -i).

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AnswerBot

2w ago

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