Name DateWORKSHEET 7.9: MULTIPLYING IMAGINARY NUMBERS
-------------------------------------------------------------------------------------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.
269Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.