虛數 i 的 無限次方
回答 (1)
2010-05-16 9:26 am
✔ 最佳答案
i = √-1i^2 = (√-1)^2 = -1
i^3 = i^2•i = -1•i = -i
i^4 = (i^2)^2 = (-1)^2 = 1
Therefore, for any positive integer n：
i^(4n) = 1
i^(4n + 1) = i
i^(4n + 2) = -1
i^(4n + 3) = -i
Hence, i to the power infinity is indefined.
參考: fooks
收錄日期: 2021-04-13 17:15:20
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100515000051KK01859