Complex Numbers P. 2
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DATE
6-8 The Complex Numbers (continued) 6
Example 3
Simplify
Solution
—5— - —1 1 + 3i
' .,-.?«.
m,
Multiply the numerator and denominator by the conjugate of the denominator. This will rationalize the denominator.
1 - 3«
I + 3i
6 -
9(-l)
1 -
1. 5
10
9. T'
Give your answer in the form a + bi.
Simplify each quotient.
16.
17.
3i
j Example 4 i
12 1-i
18.
4 + / 4 -i
19.
-2 -
Find the reciprocal of 2 - i. .'
\ Solution •
'-
The reciprocal of 2 - i is" * .. The denominator must be rationalized. Z "•** I
1 » 1 2+i 2- / 2- i ' 2+ *
'
2JL^ . _JL
Find the reciprocal of each complex number. 20- 3 + 2/ 21. 2 - Si
If fa) - 2* - -1,findA3 + 2i).
Solution
A3 -f 20 - 2(3 + 20
6 +
—r
3 + 2i 3 -2i 9 -
_ 78 + 52i 13 „„ 75 54 . 13 13*
24. If A*) * -}~ + 2x, findAl -»• «)•
104
(-4)
3 - 21 13
25.
23. - V5 +
Substitute 3 + 2i for x.
3 + 2i
K _
5
22. 4
Example S
-
A
3 _— 2/ 3 — 2* -
Rationalize the denominator. Multiply.
Find a common denominator. Simplify.
- iV3).
Study Quid*, AtQEBRA AND TRIGONOMETRY, Structure and Method, Book 2 Copyright © by Houghton Mifflln Company. All righto reserved.
DATE
6-8 The Complex Numbers (continued) 6
Example 3
Simplify
Solution
—5— - —1 1 + 3i
' .,-.?«.
m,
Multiply the numerator and denominator by the conjugate of the denominator. This will rationalize the denominator.
1 - 3«
I + 3i
6 -
9(-l)
1 -
1. 5
10
9. T'
Give your answer in the form a + bi.
Simplify each quotient.
16.
17.
3i
j Example 4 i
12 1-i
18.
4 + / 4 -i
19.
-2 -
Find the reciprocal of 2 - i. .'
\ Solution •
'-
The reciprocal of 2 - i is" * .. The denominator must be rationalized. Z "•** I
1 » 1 2+i 2- / 2- i ' 2+ *
'
2JL^ . _JL
Find the reciprocal of each complex number. 20- 3 + 2/ 21. 2 - Si
If fa) - 2* - -1,findA3 + 2i).
Solution
A3 -f 20 - 2(3 + 20
6 +
—r
3 + 2i 3 -2i 9 -
_ 78 + 52i 13 „„ 75 54 . 13 13*
24. If A*) * -}~ + 2x, findAl -»• «)•
104
(-4)
3 - 21 13
25.
23. - V5 +
Substitute 3 + 2i for x.
3 + 2i
K _
5
22. 4
Example S
-
A
3 _— 2/ 3 — 2* -
Rationalize the denominator. Multiply.
Find a common denominator. Simplify.
- iV3).
Study Quid*, AtQEBRA AND TRIGONOMETRY, Structure and Method, Book 2 Copyright © by Houghton Mifflln Company. All righto reserved.
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