130 CHAPTER 1 Equations and Inequalities 35. 2-24 28 36. 2-54 227 37. 2-10 2-40 38. 2-8 2-72 39. 2-6 # 2-2 23 40. 2-12 # 2-6 28 Write each number in standard form a + bi. See Example 3. 41. -6 - 2-24 2 42. -9 - 2-18 3 43. 10 + 2-200 5 44. 20 + 2-8 2 45. -3 + 2-18 24 46. -5 + 2-50 10 Find each sum or difference. Write answers in standard form. See Example 4. 47. 13 + 2i2 + 19 - 3i2 48. 14 - i2 + 18 + 5i2 49. 1-2 + 4i2 - 1-4 + 4i2 50. 1-3 + 2i2 - 1-4 + 2i2 51. 12 - 5i2 - 13 + 4i2 - 1-2 + i2 52. 1-4 - i2 - 12 + 3i2 + 1-4 + 5i2 53. -i 22 - 2 - A6 - 4i 22B - A5 - i 22B 54. 327 - A427 - iB - 4i + A -227 + 5iB Find each product. Write answers in standard form. See Example 5. 55. 12 + i213 - 2i2 56. 1-2 + 3i214 - 2i2 57. 12 + 4i21-1 + 3i2 58. 11 + 3i212 - 5i2 59. 13 - 2i22 60. 12 + i22 61. 13 + i213 - i2 62. 15 + i215 - i2 63. 1-2 - 3i21-2 + 3i2 64. 16 - 4i216 + 4i2 65. A 26 + iB A 26 - iB 66. A 22 - 4iB A 22 + 4iB 67. i13 - 4i213 + 4i2 68. i12 + 7i212 - 7i2 69. 3i12 - i22 70. -5i14 - 3i22 71. 12 + i212 - i214 + 3i2 72. 13 - i213 + i212 - 6i2 Find each quotient. Write answers in standard form. See Example 6. 73. 6 + 2i 1 + 2i 74. 14 + 5i 3 + 2i 75. 2 - i 2 + i 76. 4 - 3i 4 + 3i 77. 1 - 3i 1 + i 78. -3 + 4i 2 - i 79. -5 i 80. -6 i 81. 8 -i 82. 12 -i 83. 2 3i 84. 5 9i (Modeling) Alternating Current Complex numbers are used to describe current I, voltage E, and impedance Z (the opposition to current). These three quantities are related by the equation E = IZ, which is known as Ohm’s Law. Thus, if any two of these quantities are known, the third can be found. In each exercise, solve the equation E = IZ for the remaining value. 85. I = 5 + 7i, Z = 6 + 4i 86. I = 20 + 12i, Z = 10 - 5i 87. I = 10 + 4i, E = 88 + 128i 88. E = 57 + 67i, Z = 9 + 5i
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