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Exercises 12.6, page 363

1. $5.09 (\cos 258.7 ° + j \sin 258.7 °)$ $5.09 (\cos 258.7 ° + j \sin 258.7 °)$
3. $613 (\cos 281.5 ° + j \sin 281.5 °)$ $613 (\cos 281.5 ° + j \sin 281.5 °)$
5. $8 (\cos 80 ° + j \sin 80 °)$ $8 (\cos 80 ° + j \sin 80 °)$
7. $3 (\cos 250 ° + j \sin 250 °)$ $3 (\cos 250 ° + j \sin 250 °)$
9. $2 (\cos 35 ° + j \sin 35 °)$ $2 (\cos 35 ° + j \sin 35 °)$
11. $2.4 ∠ \underline{170 °}$ $2.4 ∠ \underline{170 °}$
13. $0.008 (\cos 105 ° + j \sin 105 °)$ $0.008 (\cos 105 ° + j \sin 105 °)$
15. $256 (\cos 0 ° + j \sin 0 °)$ $256 (\cos 0 ° + j \sin 0 °)$
17. $0.8 ∠ \underline{273 °}$ $0.8 ∠ \underline{273 °}$
19. $5 ∠ \underline{87 °}$ $5 ∠ \underline{87 °}$
21. $1.73 ∠ \underline{79.8 °}$ $1.73 ∠ \underline{79.8 °}$
23. $11,750 ∠ \underline{115.91 °}$ $11,750 ∠ \underline{115.91 °}$
25. $65.0 (\cos 345.7 ° + j \sin 345.7 °) = 63 - 16 j$ $65.0 (\cos 345.7 ° + j \sin 345.7 °) = 63 - 16 j$
27. $61.4 (\cos 343.9 ° + j \sin 343.9 °); 59 - 17 j$ $61.4 (\cos 343.9 ° + j \sin 343.9 °); 59 - 17 j$
29. $2.21 (\cos 71.6 ° + j \sin 71.6 °); \frac{7}{10} + \frac{21}{10} j$ $2.21 (\cos 71.6 ° + j \sin 71.6 °); \frac{7}{10} + \frac{21}{10} j$
31. $3.85 (\cos 120.5 ° + j \sin 120.5 °) = \frac{10}{169} (- 33 + 56 j)$ $3.85 (\cos 120.5 ° + j \sin 120.5 °) = \frac{10}{169} (- 33 + 56 j)$
33. $625 (\cos 212.5 ° + j \sin 212.5 °) = - 527 - 336 j$ $625 (\cos 212.5 ° + j \sin 212.5 °) = - 527 - 336 j$
35. $2 (\cos 30 ° + j \sin 30 °); 2 (\cos 210 ° + j \sin 210 °)$ $2 (\cos 30 ° + j \sin 30 °); 2 (\cos 210 ° + j \sin 210 °)$
37. $- 0.364 + 1.67 j, - 1.26 - 1.15 j, 1.63 - 0.520 j$ $- 0.364 + 1.67 j, - 1.26 - 1.15 j, 1.63 - 0.520 j$
39. $1.10 + 0.455 j, - 1.10 - 0.455 j$ $1.10 + 0.455 j, - 1.10 - 0.455 j$
41. $1, - 1, j, - j$ $1, - 1, j, - j$
43. $3 j, - \frac{3}{2} (\sqrt{3} + j), \frac{3}{2} (\sqrt{3} - j)$ $3 j, - \frac{3}{2} (\sqrt{3} + j), \frac{3}{2} (\sqrt{3} - j)$
45. $\begin{array}{l} 1.62 + 1.18 j, - 0.618 + 1.90 j, - 2, - 0.618 - 0.190 j, \\ 1.62 - 1.18 j \end{array}$ $\begin{array}{l} 1.62 + 1.18 j, - 0.618 + 1.90 j, - 2, - 0.618 - 0.190 j, \\ 1.62 - 1.18 j \end{array}$
47. $- 5, \frac{5}{2} + j \frac{5 \sqrt{3}}{2}, \frac{5}{2} - j \frac{5 \sqrt{3}}{2}$ $- 5, \frac{5}{2} + j \frac{5 \sqrt{3}}{2}, \frac{5}{2} - j \frac{5 \sqrt{3}}{2}$
49.

$\begin{array}{l} {[\frac{1}{2} (1 - j \sqrt{3})]}^{3} = \frac{1}{8} [1 - 3 (j \sqrt{3}) + 3 {(j \sqrt{3})}^{2} \\ - {(j \sqrt{3})}^{3}] = \frac{1}{8} [1 - 3 j \sqrt{3} - 9 + 3 j \sqrt{3}] \\ = \frac{1}{8} (- 8) = - 1 \end{array}$ $\begin{array}{l} {[\frac{1}{2} (1 - j \sqrt{3})]}^{3} = \frac{1}{8} [1 - 3 (j \sqrt{3}) + 3 {(j \sqrt{3})}^{2} \\ - {(j \sqrt{3})}^{3}] = \frac{1}{8} [1 - 3 j \sqrt{3} - 9 + 3 j \sqrt{3}] \\ = \frac{1}{8} (- 8) = - 1 \end{array}$
51. $- 1, \frac{1}{2} + j \frac{\sqrt{3}}{2}, \frac{1}{2} - j \frac{\sqrt{3}}{2}$ $- 1, \frac{1}{2} + j \frac{\sqrt{3}}{2}, \frac{1}{2} - j \frac{\sqrt{3}}{2}$
53. $p = 0.479 ∠ \underline{40.5 °} watts$ $p = 0.479 ∠ \underline{40.5 °} watts$
55. $43.3 ∠ \underline{165 °}, 43.3 V$ $43.3 ∠ \underline{165 °}, 43.3 V$

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Table of Contents for Exercises 12.6, page 363

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Table of Contents for
Exercises 12.6, page 363