Complex number
2012-09-14 6:12 am
Let a and b be non-zero real numbers. If the result of (a+bi)(-10+25i) is real number, find a : b.
回答 (1)
2012-09-14 6:42 am
✔ 最佳答案
(a + bi)(-10 + 25i)= a(-10 + 25i) + bi(-10 + 25i)
= -10a + 25ai - 10bi - 25b
= (-10a - 25b) + (25a - 10b)i
Since (-10a - 25b) + (25a - 10b)i is real, thus
(25a - 10b)i = 0
25a - 10b = 0
25a = 10b
5a = 2b
a/b = 2/5
a :b = 2 : 5
參考: micatkie
收錄日期: 2021-04-13 18:58:42
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