How many roots (include complex roots) are there in x^√2 = 1
2008-11-23 4:39 am
How many roots (include complex roots) are there in the equation x√2 = 1? Explain in detail.
回答 (2)
2008-11-23 8:39 am
✔ 最佳答案
z^√2=1z=cis(2kπ/√2)=cis(√2 kπ) where k is integer
since √2 is irrational, √2 kπ will never repeat,
therefore there is infinitely many roots.
參考: ME
2008-11-23 9:21 am
suppose x be the complex number,the index of the complex number x indicate the number of roots,but we cannot say that there are √2 roots,the number of roots should be an integer!Therefore,there is no complex root.
The question should be solved by the simple method:
x√2 = 1
(√2)logx = log1
(√2)logx = 0
logx = 0
x=1
The only root is 1
The question should be solved by the simple method:
x√2 = 1
(√2)logx = log1
(√2)logx = 0
logx = 0
x=1
The only root is 1
收錄日期: 2021-04-30 01:09:31
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http://hk.knowledge.yahoo.com/question/question?qid=7008112201901