Exercises 12.2, page 351

1. $1 - 5 j$
3. $\frac{1}{25} (29 + 22 j)$
5. $5 - 8 j$
7. $- 25 + 10 j$
9. $- 0.23 + 0.86 j$
11. $- 36 + 21 j$
13. $7 + 49 j$
15. $22 + 3 j$
17. $- 18 j \sqrt{2}$
19. $22 - 7 j$
21. $3 \sqrt{7} + 3 j$
23. $- 40 - 42 j$
25. 73
27. $\frac{1}{29} (- 30 + 12 j)$
29. $- \frac{1}{3} (1 + j)$
31. $\frac{1}{11} (- 13 + 8 j \sqrt{2})$
33. $\frac{- 1 + 3 j}{5}$
35. $\frac{- 45}{13} + \frac{48 j}{13}$
37. $- 8 j$
39. $- 80 j$
41. $- \frac{7}{8} + 4 j$
43. ${(- 1 - j)}^{2} + 2 (- 1 - j) + 2 = 1 + 2 j - 1 - 2 - 2 j + 2 = 0$
45. 4
47. 10
49. $\frac{3}{10} + \frac{1}{10} j$
51. $- 1 + j$
53. $- 4$
55. $\frac{1}{10} (11 + 27 j)$
57. $281 + 35.2 j volts$
59. $0.016 + 0.037 j amperes$
61.
1. Real
2. Pure imaginary
63. Product is sum of squares of two real numbers $(a + b j) (a - b j) = a^{2} + b^{2}$

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans