a) Let a be a real number . If the result of (2a+7i)-(12-4i) is a pure imaginary number, find the value of a.
b) Let a and b be non-zero real numbers. If the result of (a+bi)(-10+25i) is a real number, find a:b.
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F.4 maths ! Thanks !
2012-09-17 1:54 am
回答 (2)
2012-09-17 2:19 am
✔ 最佳答案
(2a+7i)-(12-4i)= (2a-12)+11i
If the result is a pure imaginary number, then (2a-12) is zero.
That is a=6. (Ans)
(a+bi)(-10+25i)
= (-10a-25b)+(25a-10b)i
If the result is a real number, then (25a-10b) is zero, that is
25a = 10b
5a = 2b
a : b = 2：5 (Ans)
2012-09-17 2:13 am
(2a+7i)-(12-4i)
=(2a+7i)(-12+4i) (i guess)
=-24a - 84i + 8ai -28
-24a = 28
a=-(7/6)
(a+bi)(-10+25i)
=-10a+25ai-10bi-25b
25ai-10bi=0
25a-10b=0
a=2 b=5
=(2a+7i)(-12+4i) (i guess)
=-24a - 84i + 8ai -28
-24a = 28
a=-(7/6)
(a+bi)(-10+25i)
=-10a+25ai-10bi-25b
25ai-10bi=0
25a-10b=0
a=2 b=5
參考: 自己
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