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8.9E: Mazoezi

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    176337

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    Mazoezi hufanya kamili

    Mazoezi 1 - 4: Tathmini Mizizi ya Mraba ya Idadi Hasi

    Katika mazoezi yafuatayo, andika kila kujieleza kwa suala la\(i\) na kurahisisha iwezekanavyo.

    1. a.\(\sqrt{-16}\) b.\(\sqrt{-11}\) c.\(\sqrt{-8}\)
    2. a.\(\sqrt{-121}\) b.\(\sqrt{-1}\) c.\(\sqrt{-20}\)
    3. a.\(\sqrt{-100}\) b.\(\sqrt{-13}\) c.\(\sqrt{-45}\)
    4. a.\(\sqrt{-49}\) b.\(\sqrt{-15}\) c.\(\sqrt{-75}\)
    Jibu

    1. a.\(4i\) b.\(i\sqrt{11}\) c.\(2i\sqrt{2}\)

    3. a.\(10i\) b.\(i\sqrt{13}\) c.\(3i\sqrt{5}\)

    Mazoezi 5 - 21: Ongeza au Ondoa Hesabu Complex

    Katika mazoezi yafuatayo, ongeza au uondoe, kuweka jibu kwa\(a + bi\) fomu.

    5. \(\sqrt{-75}+\sqrt{-48}\)

    6. \(\sqrt{-12}+\sqrt{-75}\)

    7. \(\sqrt{-50}+\sqrt{-18}\)

    8. \(\sqrt{-72}+\sqrt{-8}\)

    9. \((1+3 i)+(7+4 i)\)

    10. \((6+2 i)+(3-4 i)\)

    11. \((8-i)+(6+3 i)\)

    12. \((7-4 i)+(-2-6 i)\)

    13. \((1-4 i)-(3-6 i)\)

    14. \((8-4 i)-(3+7 i)\)

    15. \((6+i)-(-2-4 i)\)

    16. \((-2+5 i)-(-5+6 i)\)

    17. \((5-\sqrt{-36})+(2-\sqrt{-49})\)

    18. \((-3+\sqrt{-64})+(5-\sqrt{-16})\)

    19. \((-7-\sqrt{-50})-(-32-\sqrt{-18})\)

    20. \((-5+\sqrt{-27})-(-4-\sqrt{-48})\)

    Jibu

    5. \(0+\left(9\sqrt{3}\right)i\)

    7. \(0+\left(8\sqrt{2}\right)i\)

    9. \(8+7i\)

    11. \(14+2i\)

    13. \(-2+2i\)

    15. \(8+5i\)

    17. \(7-13i\)

    19. \(25-\left(2 \sqrt{2}\right) i\)

    Mazoezi 21 - 28: Kuzidisha Idadi tata

    Katika mazoezi yafuatayo, kuzidisha, kuweka jibu kwa\(a+bi\) fomu.

    21. \(4 i(5-3 i)\)

    22. \(2 i(-3+4 i)\)

    23. \(-6 i(-3-2 i)\)

    24. \(-i(6+5 i)\)

    25. \((4+3 i)(-5+6 i)\)

    26. \((-2-5 i)(-4+3 i)\)

    27. \((-3+3 i)(-2-7 i)\)

    28. \((-6-2 i)(-3-5 i)\)

    Jibu

    21. \(12+20i\)

    23. \(-12+18i\)

    25. \(-38+9 i\)

    27. \(27+15i\)

    Mazoezi 29 - 32: Kuzidisha Idadi tata

    Katika mazoezi yafuatayo, kuzidisha kutumia Bidhaa ya Mraba ya Binomial Pattern, kuweka jibu kwa\(a+bi\) fomu.

    29. \((3+4 i)^{2}\)

    30. \((-1+5 i)^{2}\)

    31. \((-2-3 i)^{2}\)

    32. \((-6-5 i)^{2}\)

    Jibu

    29. \(-7+24i\)

    31. \(-5-12i\)

    Mazoezi 33 - 46: Kuzidisha Idadi tata

    Katika mazoezi yafuatayo, kuzidisha, kuweka jibu kwa\(a+bi\) fomu.

    33. \(\sqrt{-25} \cdot \sqrt{-36}\)

    34. \(\sqrt{-4} \cdot \sqrt{-16}\)

    35. \(\sqrt{-9} \cdot \sqrt{-100}\)

    36. \(\sqrt{-64} \cdot \sqrt{-9}\)

    37. \((-2-\sqrt{-27})(4-\sqrt{-48})\)

    38. \((5-\sqrt{-12})(-3+\sqrt{-75})\)

    39. \((2+\sqrt{-8})(-4+\sqrt{-18})\)

    40. \((5+\sqrt{-18})(-2-\sqrt{-50})\)

    41. \((2-i)(2+i)\)

    42. \((4-5 i)(4+5 i)\)

    43. \((7-2 i)(7+2 i)\)

    44. \((-3-8 i)(-3+8 i)\)

    Jibu

    33. \(30i = 0 + 30i\)

    35. \(-30 = -30 + 0i\)

    37. \(-44+\left(4 \sqrt{3}\right) i\)

    39. \(-20-\left(2 \sqrt{2}\right) i\)

    41. \(5 = 5 + 0i\)

    43. \(53 = 53 + 0i\)

    Mazoezi 45 - 49: Kuzidisha Idadi tata

    Katika mazoezi yafuatayo, kuzidisha kutumia Bidhaa ya Complex Conjugates Pattern.

    45. \((7-i)(7+i)\)

    46. \((6-5 i)(6+5 i)\)

    47. \((9-2 i)(9+2 i)\)

    48. \((-3-4 i)(-3+4 i)\)

    Jibu

    45. \(50\)

    47. \(85\)

    Mazoezi 49 - 60: Gawanya Idadi tata

    Katika mazoezi yafuatayo, kugawanya, kuweka jibu kwa\(a+bi\) fomu.

    49. \(\dfrac{3+4 i}{4-3 i}\)

    50. \(\dfrac{5-2 i}{2+5 i}\)

    51. \(\dfrac{2+i}{3-4 i}\)

    52. \(\dfrac{3-2 i}{6+i}\)

    53. \(\dfrac{3}{2-3 i}\)

    54. \(\dfrac{2}{4-5 i}\)

    55. \(\dfrac{-4}{3-2 i}\)

    56. \(\dfrac{-1}{3+2 i}\)

    57. \(\dfrac{1+4 i}{3 i}\)

    58. \(\dfrac{4+3 i}{7 i}\)

    59. \(\dfrac{-2-3 i}{4 i}\)

    60. \(\dfrac{-3-5 i}{2 i}\)

    Jibu

    49. \(i = 0 + i\)

    51. \(\frac{2}{25}+\frac{11}{25} i\)

    53. \(\frac{6}{13}+\frac{9}{13} i\)

    55. \(-\frac{12}{13}-\frac{8}{13} i\)

    57. \(\frac{4}{3}-\frac{1}{3} i\)

    59. \(-\frac{3}{4}+\frac{1}{2} i\)

    Mazoezi 61 - 68: Kurahisisha Mamlaka ya\(i\)

    Katika mazoezi yafuatayo, kurahisisha.

    61. \(i^{41}\)

    62. \(i^{39}\)

    63. \(i^{66}\)

    64. \(i^{48}\)

    65. \(i^{128}\)

    66. \(i^{162}\)

    67. \(i^{137}\)

    68. \(i^{255}\)

    Jibu

    61. \(i^{41} = i^{40}\cdot i = \left(i^{4}\right)^{10}\cdot i= i\)

    63. \(i^{66} = i^{64}\cdot i^{2} = \left(i^{4}\right)^{16}\cdot (-1)= -1\)

    65. \(i^{128} = \left(i^{4}\right)^{32} = 1\)

    67. \(i^{137} = i^{136}\cdot i = \left(i^{4}\right)^{34}\cdot i = 1 \cdot i = i\)

    Mazoezi 69 - 72: Mazoezi ya kuandika

    69. Eleza uhusiano kati ya namba halisi na namba tata.

    70. Aniket kuzidisha kama ifuatavyo na alipata jibu sahihi. Ni nini kibaya na hoja zake?
    \(\begin{array}{c}{\sqrt{-7} \cdot \sqrt{-7}} \\ {\sqrt{49}} \\ {7}\end{array}\)

    71. Kwa nini\(\sqrt{-64}=8 i\) lakini\(\sqrt[3]{-64}=-4\).

    72. Eleza jinsi kugawa idadi tata ni sawa na rationalizing denominator.

    Jibu

    69. Majibu inaweza kutofautiana

    71. Majibu inaweza kutofautiana

    Self Check

    Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Jedwali lina nguzo 4 na safu 4. Mstari wa kwanza ni mstari wa kichwa na vichwa vya kichwa â € can â €, â € € confidentlyâ €, â € na baadhi ya usaidi.â €, na â € no â € “Mimi donâ €™ t kupata! â €. Safu ya kwanza ina maneno †tathmini mizizi ya mraba ya namba hasi â €, â € kuongeza au kuondoa namba tataâ €, â € € kuzidisha namba tataâ €, â € kugawanya namba tataâ €, na â € kurahisisha nguvu za iâ €. Nguzo nyingine zimeachwa tupu ili mwanafunzi aweze kuonyesha kiwango chao cha ufahamu.
    Kielelezo 8.8.15

    b Kwa kiwango cha 1-10, ungewezaje kupima ujuzi wako wa sehemu hii kwa kuzingatia majibu yako kwenye orodha? Unawezaje kuboresha hii?