Download Reteach Complex Numbers and Roots

Name
Date
Class
Reteach
LESSON
5-5
Complex Numbers and Roots
An imaginary number is the square root of a negative number.
Use the definition 1 i to simplify square roots.
Simplify.
25
25 1 Factor out 1.
25 1
Separate roots.
5 1
Simplify.
5i
Express in terms of i.
48
48 1 Factor out 1.
48 1
Separate roots.
16 3 1
Factor the perfect square.
4 3 1
Simplify.
4i 3
Imaginary
Real
Express in terms of i.
Complex numbers are numbers that can be written in the form a bi.
Write as a bi
Find 0 5i 5i
The complex conjugate of a bi is a bi.
The complex conjugate of 5i is 5i.
Express each number in terms of i.
1. 72
2. 445
3. 100
36 2 1 4 9 5 1 6i 2
12i 5
4. 5 54
5. 264
15i 6
10i
6. 98
16i
7i 2
Find each complex conjugate.
7. 9i
8. 1 4i
9. 12 i
1 4i
9i
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c05-5_rt.indd 38
38
12 i
Holt Algebra 2
12/15/05 4:38:11 PM
Process Black
Name
LESSON
5-5
Date
Class
Reteach
Complex Numbers and Roots (continued)
You can use the square root property and 1 i to solve quadratic equations with
imaginary solutions.
Solve x 2 64.
x 2 64
Take the square root of both sides.
2
Remember: 1 i 2 1
Express in terms of i.
x 8i
2
2
Check each root: 8i 64i 64 1 64
8i 2 64i 2 64 1 64
2
Solve 5x 80 0.
2
5x 80
x 16
2
2
Subtract 80 from both sides.
Divide both sides by 5.
x 16 Take the square root of both sides.
x 4i
Express in terms of i.
Check each root:
2
5 4i 80
5 16 i 2 80
80 1 80
0
2
5 4i 80
2
5 16 i 80
80 1 80
0
Solve each equation.
10. x 2 18 0
11. 6x 2 24 0
x 2 18
x 2 49
6x 2 24
x 9 2 1 x 3i 2
13. x 2 100 0
x 49
x 2i
x 7i
14. 3x 2 108 0
x 2 36
x 100
x 36
x 10i
x 6i
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c05-5_rt.indd 39
x 4
x 2 100
12. x 2 49 0
39
15. x 2 12 0
x 2 12
x 4 3 1 x 2i 3
Holt Algebra 2
12/15/05 4:38:12 PM
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