Reteach 5-5 - Humble ISD [PDF]

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

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12/15/05 4:38:12 PM Process Black

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Holt Algebra 2

5/20/06 2:40:07 PM