急! 急! F4 數學 number systems

Hi ! I am lop****** , feel happy to answer your question.

Q 1 : Find the values of the two real numbers h and kk if 2+ki=h-3i.

A 1 :

2+ki=h-3i
2+ki-ki=h-3i-ki
2+3i=h-3i-ki+3i
2+3i=h-ki
h = 2 , k = -3

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Q 2 : If (3-5i)+(a+bi)=5-i, find the Values of the real numbers a and b

A 2 :

(3-5i)+(a+bi)=5-i
3-5i+a+bi=5-i
a+bi=2+4i
a = 2 , b = 4

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Q 3 : If (2-i)(a+bi)=5+20i, where a and b are real numbers, find the values of a and b.

A 3 :

(2-i)(a+bi)=5+20i
2a+2bi-ai+b=5+20i
(2a+b)+(2b-a)i=5+20i

2a+b=5 --- (1)
2b-a=20 --- (2)

(1) × 2 - (2)

5a = -10
a = -2 --- (3)

Sub (3) into (1)

-4+b=5
b = 9

Answer : a = -2 , b = 9

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2011-08-15 11:35:19 補充：
Sorry I forgot to answer Q 4 :

If the expression (a+3i)(-2+3i) is a real number, find the value of the real number a.

A 4 :

(a+3i)(-2+3i)
= -2a + 3ai - 6i - 9
= -2a - 9 + (3a-6)i

So 3a-6 = 0
a = 2

Answer : a = 2

If the expression (a+3i)(-2+3i) is a real number
a=2
The method for Q3 does not use Simultaneous Equations,as follow:
(2-i)(a+bi)=5+20i.
(a+bi)=5+20i/(2-i)
(a+bi)=(2+i)(5+20i)/(2-i)(2+i)
(a+bi)=(10+40i+5i-20)/(5)
a+bi=(45i-10)/5
a+bi=9i-2
a+bi=-2+9i
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a=-2
b=9