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標題: 超難Maths問題 [打印本頁]

作者: oscar 時間: 13/1/2005 02:07 PM
標題: 超難Maths問題
Find i^i.
i is imaginary unit.

作者: JOHNLAM17 時間: 13/1/2005 06:18 PM
什麼來的.....
我中三ja wor=.=

作者: oscar 時間: 13/1/2005 07:18 PM

Originally posted by JOHNLAM17 at 2005-1-13 18:18:
什麼來的.....
我中三ja wor=.=

大約是大學level的數學難題

作者: 抹茶可樂 時間: 13/1/2005 07:53 PM
唔識

作者: oscar 時間: 13/1/2005 08:14 PM

Originally posted by 落雷 at 2005-1-13 19:53:
唔識

算啦...都預左冇人識....

作者: 莫邪 時間: 13/1/2005 08:15 PM

Originally posted by oscar at 13-1-2005 08:14 PM:

算啦...都預左冇人識....

咁你又問?

作者: oscar 時間: 13/1/2005 08:22 PM

Originally posted by 莫邪 at 2005-1-13 20:15:

咁你又問?

睇下落雷識唔識...

作者: JOHNLAM17 時間: 13/1/2005 09:15 PM
咁算唔算串咀

你解la

作者: pokevect 時間: 13/1/2005 09:46 PM

Originally posted by oscar at 2005-1-13 02:07 PM:
Find i^i.
i is imaginary unit.

開方-1既開方-1次方???

無啦啦問d咁既野做乜呀???

power of imaginary number is meaningless!

[ Last edited by pokevect on 2005-1-13 at 09:48 PM ]

作者: 貝貝☆ 時間: 13/1/2005 09:57 PM
0.207879576

[ Last edited by ericfong on 2005-1-13 at 10:01 PM ]

作者: JOHNLAM17 時間: 13/1/2005 10:18 PM
very 勁wor

作者: 抹茶可樂 時間: 13/1/2005 10:39 PM

Originally posted by ericfong at 2005-1-13 09:57 PM:
0.207879576

[ Last edited by ericfong on 2005-1-13 at 10:01 PM ]

要step.

作者: oscar 時間: 14/1/2005 10:32 AM
我禁cal-tor都話Math Error...

作者: snoopy11hk 時間: 17/1/2005 09:02 PM
By definition, i^i = e^(i log i)
By definition again, log i = log 1 + i * arg(i) ( here the arg is multi-valued)
so log i = 0 + (2n(pi)+(pi)/2)*i , n is an integer
so i log i = -2n(pi)-(pi)/2 , n is an integer
so i^i = e^(-2n(pi)-(pi)/2) , n is an integer

Maybe it's too difficult for a secondary school student to know these...-_-!

by Master

作者: 貝貝☆ 時間: 18/1/2005 07:14 PM

Originally posted by oscar at 2005-1-14 10:32 AM:
我禁cal-tor都話Math Error...

咁 0.207879576岩唔岩?

作者: oscar 時間: 18/1/2005 07:19 PM

Originally posted by ericfong at 2005-1-18 19:14:

咁 0.207879576岩唔岩?

錯...
答案並非一個數值來的~

作者: 抹茶可樂 時間: 18/1/2005 07:58 PM
但根據某網的計算器，是那個值，而且標明是「Real」的

作者: Royal 時間: 18/1/2005 11:58 PM

Originally posted by oscar at 2005-1-18 07:19 PM:

錯...
答案並非一個數值來的~

i^i = 0.207879576
用google計數機計出來的…""

順帶一提(要睡覺了)，根據「數學論壇」對這條數的研究，
i^i = e^(-pi/2)
其實同S生提供的那個答案很像已相近了(我還未學過這類數)，
（S生提供的答案為 i^i = e^(-2n(pi)-(pi)/2) , n is an integer）
而再用google計數機，e^(-pi/2) = 0.207879576…""
不過我無法在google計e^(-2n(pi)-(pi)/2)

詳情數式可參考：
http://mathforum.org/epigone/sci ... @posting.google.com

賣廣告：google真係好好用(個系統唔好再話我爆粗！）

作者: 貝貝☆ 時間: 19/1/2005 12:10 AM
我阿哥唔係用google ga-.-
step:
e^(ix)=cis x
put x =pi/2+2n pi

禁下cal機
finished

[ Last edited by ericfong on 2005-1-19 at 12:18 AM ]

作者: 貝貝☆ 時間: 19/1/2005 08:22 PM

Originally posted by ericfong at 2005-1-19 12:10 AM:
我阿哥唔係用google ga-.-
step:
e^(ix)=cis x
put x =pi/2+2n pi

禁下cal機
finished

[ Last edited by ericfong on 2005-1-19 at 12:18 AM ]

夠竟個答覆係唔係咁姐T_T我要同阿哥講番ga

作者: snoopy11hk 時間: 20/1/2005 09:50 PM
車里厘.....你點識 ga????? .....你唔係 F.2 ga 咩???
..............好 tough ar....

作者: oscar 時間: 20/1/2005 10:13 PM

Originally posted by ericfong at 2005-1-19 20:22:

夠竟個答覆係唔係咁姐T_T我要同阿哥講番ga

我唔知呀...
我要問番我個friend先知...

作者: snoopy11hk 時間: 20/1/2005 10:42 PM
..F.3 題??
....wt is the ans??

作者: oscar 時間: 20/1/2005 11:03 PM

Originally posted by snoopy11hk at 2005-1-20 22:42:
..F.3 題??
....wt is the ans??

form3咁難就嚇死人啦....
我個friend係form4嫁...
佢對數學好有興趣~

作者: snoopy11hk 時間: 20/1/2005 11:13 PM
wt is the ans???

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