中四-數學 MC【20點】

16.
答案是： (-47/25)+ (29/25)i

1 / (3 - 4i)
= (3 + 4i) / (3 - 4i)(3 + 4i)
= (3 + 4i) / (3² + 4²)
= (3/25) + (4/25)i

-2 + i + [1 / (3 - 4i)]
= -2 + i + (3/25) + (4/25)i
= (-47/25) + (29/25)i


=====
17.
答案是： D.a = 8，b = 2

(6 + 5i) - (a + bi) = -2 + 3i
(6 - a) + (5 - b)I = -2 + 3i

實部：
6 - a = -2
a = 8

虛部：
5 - b = 3
b = 2


=====
18.
答案是： B. -7/2

(-1 + i)(a - bi) = 4 - 3i
-a + bi + ai + b = 4 - 3i
(-a + b) + (a + b)i = 4 - 3i

實部： -a + b = 4 ...... [1]
虛部： a + b = -3 ...... [2]

[2] - [1] :
2a = -7
a = -7/2


=====
19.
答案是： D.5/29

1 / (a - bi) = -2 + 5i
(a - bi)(-2 + 5i) = 1
-2a + 5ai + 2bi + 5b = 1
(-2a + 5b) + (5a + 2b)i = 1

實部： -2a + 5b = 1 ...... [1]
虛部： 5a + 2b = 0 ...... [2]

[1]x5 + [2]x2 :
29b = 5
b = 5/29


=====
20.
答案是： A.-2

(k - ki) + (2 - i) - 3ki
= k - ki + 2 - i - 3ki
= (k + 2) - (4k + 1)i

實部 = 0
k + 2 = 0
k = -2