Exercises 12.1, page 348

  1. 1. 6

  2. 3.  − 1

  3. 5. 9j

  4. 7.  − 2j

  5. 9. 0.6j

  6. 11. 8j2

  7. 13. 12 j7

  8. 15.  − 2πjπ

  9. 17.

    1.  − 7

    2. 7

  10. 19.

    1. 4

    2.  − 4

  11. 21.  − 35

  12. 23. 10j

  13. 25.

    1. 1

    2.  − 1

  14. 27. 0

  15. 29.  − 2j

  16. 31.  − j

  17. 33. 2 + 3j

  18. 35.  − 7j

  19. 37. 2 + 2j

  20. 39.  − 2 + 3j

  21. 41. 32 − 2j2

  22. 43.  − 1

  23. 45.  − 15

  24. 47.  − 12 + 22

  25. 49. j − 2

  26. 51.

    1. 6 + 7j

    2. 8 − j

  27. 53.

    1.  − 2j

    2.  − 4

  28. 55. x = 2 ,  y =  − 2

  29. 57. x = 10 ,  y =  − 6

  30. 59. x =  − 2 ,  y = 3

  31. 61. 4j2 ,   − 4j2

  32. 63.  − 1 + j6 ,   − 1 − j6

  33. 65.

    1. No change

    2. Sign changes

  34. 67. Yes

  35. 69. 0

  36. 71. Yes; imag. part is zero.

  37. 73. Each is x.

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