19. 4x2. 20 0 i 5. 20. x2. 16 0. 4i. 21. x2. 18 0. 3i 2. 22. 8x2. 96 0. 2i 3. Find the values of m and n that make each equation true. 23. 20 12i. 5m...
NAME ______________________________________________ DATE
5-4
Skills Practice Complex Numbers
3y5 3. 兹52x 苶 苶 2| x |
2.
y 2 兹13xy 苶
5. 兹苶 ⫺81x6 9 | x 3 | i
7. (3i)(⫺2i)(5i) 30i
Practice Complex Numbers
Simplify. 1. 兹99 苶 3兹11 苶
____________ PERIOD _____
Simplify.
3兹3 苶 冑苳 ᎏ 7
3b4 1. 兹⫺36a 苶苶
27 ᎏ 49
4. 兹⫺108 苶x 苶7 6i |
2. 兹⫺8 苶 ⭈ 兹⫺32 苶
6| a| b2i 兹a 苶
x3
|兹3x 苶
4.
6. 兹⫺23 苶 ⭈ 兹⫺46 苶 ⫺23兹2 苶
冑苳
550x 15兹2x 苶 ᎏ ᎏ 49 7
5.
10.
⫺5兹15 苶
冑苳
a6b3 |a3|b兹2b 苶 ᎏ ᎏᎏ 98 14
6.
8. (7i)2(6i)
7. (⫺3i)(4i)(⫺5i)
8. i 11 ⫺i
3. 兹⫺15 苶 ⭈ 兹⫺25 苶
⫺16
⫺60i
⫺294i
i 55
i 89
11.
17 ᎏ 81
9. i 42
⫺1 12. (5 ⫺ 2i) ⫹ (⫺13 ⫺ 8i)
⫺8 ⫺ 10i
i
10. (7 ⫺ 8i) ⫹ (⫺12 ⫺ 4i) ⫺5 ⫺ 12i
13. (7 ⫺ 6i) ⫹ (9 ⫹ 11i)
14. (⫺12 ⫹ 48i) ⫹ (15 ⫹ 21i)
15. (10 ⫹ 15i) ⫺ (48 ⫺ 30i)
11. (⫺3 ⫹ 5i) ⫹ (18 ⫺ 7i) 15 ⫺ 2i
12. (10 ⫺ 4i) ⫺ (7 ⫹ 3i) 3 ⫺ 7i
16. (28 ⫺ 4i) ⫺ (10 ⫺ 30i)
17. (6 ⫺ 4i)(6 ⫹ 4i)
18. (8 ⫺ 11i)(8 ⫺ 11i)
13. (7 ⫺ 6i)(2 ⫺ 3i) ⫺4 ⫺ 33i
14. (3 ⫹ 4i)(3 ⫺ 4i) 25
8 ⫺ 6i ⫺6 ⫺ 8i ᎏ 15. ᎏ 3i 3
3 ⫹ 6i 3i 16. ᎏ ᎏ 10 4 ⫹ 2i
18 ⫹ 26i
18. 5x2 ⫹ 125 ⫽ 0 ⫾5i
19. 4x2 ⫹ 20 ⫽ 0 ⫾i 兹5 苶
20. ⫺x2 ⫺ 16 ⫽ 0 ⫾4i
21. x2 ⫹ 18 ⫽ 0 ⫾3i 兹2 苶
22. 8x2 ⫹ 96 ⫽ 0 ⫾2i 兹3 苶
Find the values of m and n that make each equation true.
Glencoe Algebra 2
23. 20 ⫺ 12i ⫽ 5m ⫹ 4ni 4, ⫺3
24. m ⫺ 16i ⫽ 3 ⫺ 2ni 3, 8
25. (4 ⫹ m) ⫹ 2ni ⫽ 9 ⫹ 14i 5, 7
26. (3 ⫺ n) ⫹ (7m ⫺ 14)i ⫽ 1 ⫹ 7i 3, 2
Chapter 5
30
3 ⫹ 69i
⫺57 ⫺ 176i
52 20. (7 ⫹ 2i)(9 ⫺ 6i)
23 ⫺ 14i 14 ⫹ 16i 2 22. ᎏ ᎏᎏ 113 7 ⫺ 8i
⫺38 ⫹ 45i
⫺5 ⫹ 6i
6 ⫹ 5i ᎏ 21. ᎏ ⫺2i 2
75 ⫺ 24i 7⫹i
3⫺i ᎏ 23. ᎏ 2⫺i 5
2 ⫺ 4i
24. ᎏ 1 ⫹ 3i ⫺1 ⫺ i
Solve each equation. 25. 5n2 ⫹ 35 ⫽ 0 ⫾i 兹7 苶
26. 2m2 ⫹ 10 ⫽ 0 ⫾i 兹5 苶
27. 4m2 ⫹ 76 ⫽ 0 ⫾i 兹19 苶
28. ⫺2m2 ⫺ 6 ⫽ 0 ⫾i 兹3 苶
29. ⫺5m2 ⫺ 65 ⫽ 0 ⫾i 兹13 苶
30. ᎏ x2 ⫹ 12 ⫽ 0 ⫾4i
3 4
Find the values of m and n that make each equation true. 31. 15 ⫺ 28i ⫽ 3m ⫹ 4ni 5, ⫺7
32. (6 ⫺ m) ⫹ 3ni ⫽ ⫺12 ⫹ 27i 18, 9
33. (3m ⫹ 4) ⫹ (3 ⫺ n)i ⫽ 16 ⫺ 3i 4, 6
34. (7 ⫹ n) ⫹ (4m ⫺ 10)i ⫽ 3 ⫺ 6i 1, ⫺4
35. ELECTRICITY The impedance in one part of a series circuit is 1 ⫹ 3j ohms and the impedance in another part of the circuit is 7 ⫺ 5j ohms. Add these complex numbers to find the total impedance in the circuit. 8 ⫺ 2j ohms
36. ELECTRICITY Using the formula E ⫽ IZ, find the voltage E in a circuit when the current I is 3 ⫺ j amps and the impedance Z is 3 ⫹ 2j ohms. 11 ⫹ 3j volts Chapter 5
31
Glencoe Algebra 2
Lesson 5-4
Chapter 5
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