869 CHAPTER 8 Review Exercises Perform each operation. Write answers in rectangular form. 53. 351cos 90° + i sin 90°24361cos 180° + i sin 180°24 54. 33 cis 135°432 cis 105°4 55. 21cos 60° + i sin 60°2 81cos 300° + i sin 300°2 56. 4 cis 270° 2 cis 90° 57. A 23 + iB 3 58. 12 - 2i25 59. 1cos 100° + i sin 100°26 60. Concept Check The vector representing a real number will lie on the -axis in the complex plane. Graph each complex number. 61. 5i 62. -4 + 2i 63. 3 - 3i23 64. Find the sum of 7 + 3i and -2 + i. Graph both complex numbers and their resultant. Write each complex number in its alternative form, using a calculator to approximate answers to four decimal places as necessary. Rectangular Form Trigonometric Form 65. -2 + 2i 66. 31cos 90° + i sin 90°2 67. 21cos 225° + i sin 225°2 68. -4 + 4i23 69. 1 - i 70. 4 cis 240° 71. -4i 72. 7 cis 310° Concept Check The complex number z, where z = x + yi , can be graphed in the plane as 1x, y2. Describe the graph of all complex numbers z satisfying the given conditions. 73. The imaginary part of z is the negative of the real part of z. 74. The absolute value of z is 2. Find all roots as indicated. Write answers in trigonometric form. 75. the cube roots of 1 - i 76. the fifth roots of -2 + 2i 77. Concept Check How many real sixth roots does -64 have? 78. Concept Check How many real fifth roots does -32 have? Find all complex number solutions of each equation. Write answers in trigonometric form. 79. x4 + 16 = 0 80. x3 + 125 = 0 81. x2 + i = 0 82. Convert 15, 315°2 to rectangular coordinates. 83. Convert A -1, 23 B to polar coordinates, with 0° … u 6360° and r 70. 84. Concept Check Describe the graph of r = k for k 70. Identify and graph each polar equation for u in 30°, 360°2. 85. r = 4 cos u 86. r = -1 + cos u 87. r = 2 sin 4u 88. r = 2 2 cos u - sin u
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