Answer Key 9.9

  1. 3+8-4i
    11-4i
  2. 3i-7i
    -4i
  3. 7i-3+2i
    9i-3
  4. 5-6-6i
    -1-6i
  5. -6i-3-7i
    -13i-3
  6. -8i-7i-5+3i
    -12i-5
  7. 3-3i-7-8i
    -4-11i
  8. -4-i+1-5i
    -3-6i
  9. i-2-3i-6
    -2i-8
  10. 5-4i+8-4i
    13-8i
  11. -48i^2
    -48(-1)
    48
  12. -24i^2
    -24(-1)
    24
  13. -40i^2
    -40(-1)
    40
  14. -32i^2
    -32(-1)
    32
  15. 49i^2
    49(-1)
    -49
  16. -7i^2(4-3i)
    -28i^2+21i^3
    -28(-1)+21(-1)i
    28-21i
  17. 36+60i+25i^2
    36+60i+25(-1)
    36+60i-25
    11+60i
  18. 16i^2(-2-8i)
    32i^2+128i^3
    32(-1)+128(-1)i
    -32-128i
  19. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ &56&-&42i&& \\ &&+&32i&-&24i^2 \\ \midrule &56&-&10i&-&24(-1) \\ +&24&&&\Longleftarrow & \\ \midrule &80&-&10i&& \end{array}
  20. 9i^2(4-4i)
    -36i^2+36i^3
    -36(-1)+36(-1)i
    36-36i
  21. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ &-8&+&10i&& \\ &&+&28i&-&35i^2 \\ \midrule &-8&+&38i&-&35(-1) \\ +&35&&&\Longleftarrow & \\ \midrule &27&+&38i&& \end{array}
  22. -32i+64i+4+12i
    -28+76i
  23. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ &32&+&24i&& \\ &&-&16i&-&12i^2 \\ \midrule &32&+&8i&-&12(-1) \\ +&12&&&\Longleftarrow & \\ \midrule &44&+&8i&& \end{array}
  24. -18i+12i^2-28i^2
    -18i+12(-1)-28(-1)
    -18i-12+28
    -18i+16
  25. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ &2&+&10i&& \\ &&+&i&+&5i^2 \\ \midrule &2&+&11i&+&5(-1) \\ -&5&&&\Longleftarrow & \\ \midrule &-3&+&11i&& \end{array}
  26. \begin{array}{rrrrrl} \\ \\ \\ \\ \\ &-6&+&3i&& \\ &&+&10i&-&5i^2 \\ \midrule &-6&+&13i&-&5(-1) \\ +&5&&&\Longleftarrow & \\ \midrule &-1&+&13i&& \end{array}
  27. \dfrac{-9+5i}{i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-9i+5i^2}{i^2}\Rightarrow \dfrac{-9i+5(-1)}{(-1)}\Rightarrow 9i+5
  28. \dfrac{-3+2i}{-3i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-3i+2i^2}{-3i^2}\Rightarrow \dfrac{-3i+2(-1)}{-3(-1)}\Rightarrow \dfrac{-3i-2}{3}
  29. \dfrac{-10i-9i}{6i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-10i-9i^2}{6i^2}\Rightarrow \dfrac{-10i-9(-1)}{6(-1)}\Rightarrow \dfrac{-10i+9}{-6}
  30. \dfrac{-4+2i}{3i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-4i+2i^2}{3i^2}\Rightarrow \dfrac{-4i+2(-1)}{3(-1)}\Rightarrow \dfrac{-4i-2}{-3}
  31. \dfrac{-3-6i}{4i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-3i-6i^2}{4i^2}\Rightarrow \dfrac{-3i-6(-1)}{4(-1)}\Rightarrow \dfrac{-3i+6}{4}
  32. \dfrac{-5+9i}{9i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{-5i+9i^2}{9i^2}\Rightarrow \dfrac{-5i+9(-1)}{9(-1)}\Rightarrow \dfrac{-5i-9}{-9}\Rightarrow \dfrac{5i+9}{9}
  33. \dfrac{10-i}{-i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{10i-i^2}{-i^2}\Rightarrow \dfrac{10i-(-1)}{-(-1)}\Rightarrow 10i+1
  34. \dfrac{10}{5i}\cdot \dfrac{i}{i}\Rightarrow \dfrac{10i}{5i^2}\Rightarrow \dfrac{10i}{5(-1)}\Rightarrow \dfrac{10i\div -5}{-5\div -5}\Rightarrow -2i
  35. \dfrac{4i}{-10+i}\cdot \dfrac{-10-i}{-10-i}\Rightarrow \dfrac{-40i-4i^2}{(-10)^2-(i)^2}\Rightarrow \dfrac{-40i-4(-1)}{100--1}\Rightarrow \dfrac{-40i+4}{101}
  36. \dfrac{9i}{1-5i}\cdot \dfrac{1+5i}{1+5i}\Rightarrow \dfrac{9i+45i^2}{(1)^2-(5i)^2}\Rightarrow \dfrac{9i+45(-1)}{1-25i^2}\Rightarrow \dfrac{9i-45}{1-25(-1)}\Rightarrow \dfrac{9i-45}{1+25}\Rightarrow \\
    \dfrac{9i-45}{26}
  37. \dfrac{8}{7-6i}\cdot \dfrac{7+6i}{7+6i}\Rightarrow \dfrac{56+48i}{7^2-36i^2}\Rightarrow \dfrac{56+48i}{49-36(-1)}\Rightarrow \dfrac{56+48i}{49+36}\Rightarrow \dfrac{56+48i}{85}
  38. \dfrac{4}{4+6i}\cdot \dfrac{4-6i}{4-6i}\Rightarrow \dfrac{16-24i}{16-36i^2}\Rightarrow \dfrac{16-24i}{16+36}\Rightarrow \dfrac{(16-24i)\div 4}{52\div 4} \Rightarrow \dfrac{4-6i}{13}
  39. \dfrac{7}{10-7i}\cdot \dfrac{10+7i}{10+7i}\Rightarrow \dfrac{70+49i}{100-49i^2}\Rightarrow \dfrac{70+49i}{100+49}\Rightarrow \dfrac{70+49i}{149}
  40. \dfrac{9}{-8-6i}\cdot \dfrac{-8+6i}{-8+6i}\Rightarrow \dfrac{-72+54i}{64-36i^2}\Rightarrow \dfrac{-72+54i}{64+36}\Rightarrow \dfrac{(-72+54i)\div 2}{100\div 2}\Rightarrow \\
    \dfrac{-36+27i}{50}
  41. \dfrac{5i}{-6-i}\cdot \dfrac{-6+i}{-6+i}\Rightarrow \dfrac{-30i+5i^2}{36-i^2}\Rightarrow \dfrac{-30i-5}{36+1}\Rightarrow \dfrac{-30i-5}{37}
  42. \dfrac{8i}{6-7i}\cdot \dfrac{6+7i}{6+7i}\Rightarrow \dfrac{48i+56i^2}{36-49i^2}\Rightarrow \dfrac{48i-56}{36+49}\Rightarrow \dfrac{48i-56}{85}
  43. \pm 9i
  44. \sqrt{-5\cdot 9}\Rightarrow \pm 3\sqrt{5}i
  45. \sqrt{-20}\Rightarrow \sqrt{-4\cdot 5}\Rightarrow \pm2\sqrt{5}i
  46. \sqrt{24}\Rightarrow \sqrt{4\cdot 6}\Rightarrow \pm 2\sqrt{6}
  47. \dfrac{3+\sqrt{3\cdot -9}}{6}\Rightarrow \dfrac{3+3\sqrt{3}i}{6}\Rightarrow \dfrac{1+\sqrt{3}i}{2}
  48. \dfrac{-4-\sqrt{-2\cdot 4}}{-4}\Rightarrow \dfrac{-4-2\sqrt{2}i}{-4}\Rightarrow \dfrac{2+\sqrt{2}i}{2}
  49. \dfrac{8-4i}{4}\Rightarrow 2-i
  50. \dfrac{6+\sqrt{2\cdot -16}}{4}\Rightarrow \dfrac{6+4\sqrt{2}i}{4}\Rightarrow \dfrac{3+2\sqrt{2}i}{2}
  51. i
  52. i^3\Rightarrow -i
  53. 1
  54. 1
  55. i^2\Rightarrow -1
  56. i
  57. i^2\Rightarrow -1
  58. i^3\Rightarrow -i

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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