更新1:
講小左 係要乘上去 i x i^2 x i^3................i^2010 =.= 再答我 .....thx~
復數 乘法~快
2010-10-16 12:36 am
i=開方 -1 [ i^2= -1] [ i^3 = i] [ i^4= (-1)] ............照咁乘上去 ...咁i^2010 等於幾多? 10點!!
回答 (2)
2010-10-16 12:40 am
✔ 最佳答案
i ^2010 = ( i^2 ) ^ 1005
= -1 ^ 1005
= -1
2010-10-15 17:09:06 補充：
And i^4 = 1 , not -1 , OK?
2010-10-30 20:26:37 補充：
i x i^2 x i^3................i^2010
= i ^ ( 1 + 2 + 3 + ... + 2009 + 2010 )
= i ^ [ ( 1 + 2010 ) 2010 / 2 ]
= i ^ [ 2011 x 1005 ]
= i ^ 2021055
= i^2 ^ 1010527 x i^1
= -1 ^ 1010527 x i
= ( -1 x -1 ) ^ 505263 x -1^1 x i
= 1 ^ 505263 x -1 x i
= 1 x -1 x i
= -1 x i
= -i
2010-10-16 12:41 am
Since i^4 = 1, so i^2010 = i^(4 x 502 + 2) = [(i^4)^502] [ i^2 ]= i^2 = - 1.
收錄日期: 2021-04-25 22:38:22
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101015000051KK00764