complex number- conjugate pair

👨🏻‍🏫 學術台數學

Mabel

2010-05-23 4:39 am

當搵roots ge時候...solutions幾時會係conjugate pairs?
係咪一定會係conjugate??

更新1:

i came across a question like this: Find, in Cartesian form, all complex fourth roots of -8 + 8(sqrt 3)i however, the solutions are sqrt3 + i -1 + sqrt 3i -sqrt3 - i 1 - sqrt 3i so are they conjugate pairs!!? even the signs in front of the real number part is different!!

回答 (2)

用戶10012

2010-05-23 6:14 am

✔ 最佳答案

1. Roots will be in complex conjugate pairs only if the ' number ' is real because
the sum of conjugate pair is real, also the product of conjugate pair is real.
2. However, - 8 + 8 sqrt3 i is not a real number but a complex number, so you cannot expect its roots are in conjugate pair.

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STEVIE-G™

2010-05-23 5:15 am

Yes.
If a+bi is a root of f(x)=0, then a-bi is also a root of f(x).

2010-05-22 21:42:01 補充：
-1 + sqrt 3i and 1 - sqrt 3i are not conjugate pairs...

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收錄日期: 2021-04-22 00:48:06
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