求數學高手實數與虛數

👨🏻‍🏫 學術台數學

[匿名]

2011-09-08 5:58 am

己知 (4+8i)-(9-4bi) 的結果是實數, 永實數 b 的值!!

回答 (3)

徐偉國

2011-09-08 6:09 am

✔ 最佳答案

(4+8i)-(9-4bi)=4+8i-9+4bi=(8+4b)i-5
8+4b=0
b=-2

參考: me

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sir

2011-09-08 7:42 pm

己知 (4+8i)-(9-4bi) 的結果是實數, 求實數 b 的值!!

Let z = (4+8i)-(9-4bi)

z = -5 + (8+4b)i

Since z is a real number,

Im z = 0

=> 8 + 4b = 0

=> b = -2

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Gary

2011-09-08 6:18 am

since answer is 實數, i will be eliminated,

then:
(4+8i)-(9-4bi) = n+0i
=> 8i +4bi=0i
=> 8+4b=0
=> b=-2

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