唔該各位高人幫我睇下以下2條數:
1. It is given that (a+bi)+(2-i) = 2b-ai, where a and b are real numbers. Find the values of a and b.
2.Let a and b be non-zero real numbers. If the result of (a+bi)(-10+25i) is a real number, find a:b.
(If neccesary, a= 6)
(f4 maths) number system
2009-09-18 4:42 am
回答 (1)
2009-09-18 5:04 am
✔ 最佳答案
(1) (a + bi) + (2 - i) = 2b - ai(a + 2) + (b - 1)i = 2b - ai
Equating real and imaginary parts separately,
a + 2 = 2b ... (1)
b - 1 = -a ... (2)
(2) => b = 1 - a
Sub into (1), a + 2 = 2(1 - a)
a + 2 = 2 - 2a
a = 0 => b = 1
(2) (a + bi)(-10 + 25i)
= a(-10 + 25i) + bi(-10 + 25i)
= -10a + 25ai - 10bi - 25b
= (-10a - 25b) + (25a - 10b)i, is a real number
=> imaginary part = 0
=> 25a - 10b = 0
=> 25a = 10b
=> a = 2b/5
a : b = 2b/5 : b = 2 : 5
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