how to evaluate a^b,where a and b are complex no.?
such as (1+i)^(2+i)
a^b,where a and b are complex no.
2007-12-30 4:40 am
回答 (1)
2007-12-30 5:09 am
✔ 最佳答案
這需要用到極式 (Polar form) 和歐拉式 (Euler's form) 和它們之間的轉換. 首先:圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Dec07/Crazycomp1.jpg
其中 θ 是以弧度 (radian) 量度的.
然後:
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Dec07/Crazycomp2.jpg
Note: 使用 Euler formula 時並無限制的, 從 e^(iπ) = -1 便可得知, 因為 π 是 irrational no.
參考: My Maths knowledge and http://hk.knowledge.yahoo.com/question/?qid=7007121801367
收錄日期: 2021-04-25 17:19:08
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