Name Date
WORKSHEET 7.9: MULTIPLYING IMAGINARY NUMBERS
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To multiply imaginary numbers, follow the steps below:
- Factor
√
− 1 from the negative radicands.
- Substitute
√
− 1 withi.
- Multiply the radicands and simplify the product.
- Multiply thei’s using the patterni=
√
−1,i^2 =−1,i^3 =− 1
√
− 1 =−i,i^4 = 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
- i^5 5. −
√
− 16 6. i
√
− 2 ·
√
− 4
- 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
√
- Her work is incorrect. What
could be her mistake? Provide the correct answer.
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.