The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

(Marvins-Underground-K-12) #1
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WORKSHEET 7.9: MULTIPLYING IMAGINARY NUMBERS
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To multiply imaginary numbers, follow the steps below:


  1. Factor



− 1 from the negative radicands.


  1. Substitute



− 1 withi.


  1. Multiply the radicands and simplify the product.

  2. Multiply thei’s using the patterni=



−1,i^2 =−1,i^3 =− 1


− 1 =−i,i^4 = 1 ,...


  1. Multiply the numbers preceding the radicals.


EXAMPLES

− 2 ·


− 3 =


− 1 ·


2 ·


− 1 ·


3 =i


2 ·i


3 =i^2


6 =−


6

6


7 ·


− 8 = 6


7 ·


− 1 ·


8 = 6 i


56 = 6 i


4 ·


14 = 6 i· 2


14 = 12 i


14

DIRECTIONS: Simplify each expression.







− 3 ·


12 2.



− 4 ·


− 25 3.



− 2 ·


− 3


  1. i^5 5. −



− 16 6. i



− 2 ·


− 4


  1. 3 i· 2 i 8. 3



2 ·


− 20 9. 4



2 ·


− 30





20 ·


− 4 11.



− 3 ·


− 27 12. − 4 i·− 5 i


CHALLENGE:√ Vicky completed this problem:
− 2 ·


− 10 =


− 2 ·− 10 =


20 = 2



  1. Her work is incorrect. What
    could be her mistake? Provide the correct answer.


269

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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