{"id":1970,"date":"2021-12-02T19:40:15","date_gmt":"2021-12-03T00:40:15","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-9\/"},"modified":"2023-09-01T14:52:12","modified_gmt":"2023-09-01T18:52:12","slug":"answer-key-9-9","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-9\/","title":{"raw":"Answer Key 9.9","rendered":"Answer Key 9.9"},"content":{"raw":"
    \r\n \t
  1. [latex]3+8-4i[\/latex]\r\n[latex]11-4i[\/latex]<\/li>\r\n \t
  2. [latex]3i-7i[\/latex]\r\n[latex]-4i[\/latex]<\/li>\r\n \t
  3. [latex]7i-3+2i[\/latex]\r\n[latex]9i-3[\/latex]<\/li>\r\n \t
  4. [latex]5-6-6i[\/latex]\r\n[latex]-1-6i[\/latex]<\/li>\r\n \t
  5. [latex]-6i-3-7i[\/latex]\r\n[latex]-13i-3[\/latex]<\/li>\r\n \t
  6. [latex]-8i-7i-5+3i[\/latex]\r\n[latex]-12i-5[\/latex]<\/li>\r\n \t
  7. [latex]3-3i-7-8i[\/latex]\r\n[latex]-4-11i[\/latex]<\/li>\r\n \t
  8. [latex]-4-i+1-5i[\/latex]\r\n[latex]-3-6i[\/latex]<\/li>\r\n \t
  9. [latex]i-2-3i-6[\/latex]\r\n[latex]-2i-8[\/latex]<\/li>\r\n \t
  10. [latex]5-4i+8-4i[\/latex]\r\n[latex]13-8i[\/latex]<\/li>\r\n \t
  11. [latex]-48i^2[\/latex]\r\n[latex]-48(-1)[\/latex]\r\n[latex]48[\/latex]<\/li>\r\n \t
  12. [latex]-24i^2[\/latex]\r\n[latex]-24(-1)[\/latex]\r\n[latex]24[\/latex]<\/li>\r\n \t
  13. [latex]-40i^2[\/latex]\r\n[latex]-40(-1)[\/latex]\r\n[latex]40[\/latex]<\/li>\r\n \t
  14. [latex]-32i^2[\/latex]\r\n[latex]-32(-1)[\/latex]\r\n[latex]32[\/latex]<\/li>\r\n \t
  15. [latex]49i^2[\/latex]\r\n[latex]49(-1)[\/latex]\r\n[latex]-49[\/latex]<\/li>\r\n \t
  16. [latex]-7i^2(4-3i)[\/latex]\r\n[latex]-28i^2+21i^3[\/latex]\r\n[latex]-28(-1)+21(-1)i[\/latex]\r\n[latex]28-21i[\/latex]<\/li>\r\n \t
  17. [latex]36+60i+25i^2[\/latex]\r\n[latex]36+60i+25(-1)[\/latex]\r\n[latex]36+60i-25[\/latex]\r\n[latex]11+60i[\/latex]<\/li>\r\n \t
  18. [latex]16i^2(-2-8i)[\/latex]\r\n[latex]32i^2+128i^3[\/latex]\r\n[latex]32(-1)+128(-1)i[\/latex]\r\n[latex]-32-128i[\/latex]<\/li>\r\n<\/ol>\r\n
      \r\n \t
    1. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrl}\r\n&56&-&42i&& \\\\\r\n&&+&32i&-&24i^2 \\\\\r\n\\hline\r\n&56&-&10i&-&24(-1) \\\\\r\n+&24&&&\\Longleftarrow & \\\\\r\n\\hline\r\n&80&-&10i&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
    2. [latex]9i^2(4-4i)[\/latex]\r\n[latex]-36i^2+36i^3[\/latex]\r\n[latex]-36(-1)+36(-1)i[\/latex]\r\n[latex]36-36i[\/latex]<\/li>\r\n \t
    3. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrl}\r\n&-8&+&10i&& \\\\\r\n&&+&28i&-&35i^2 \\\\\r\n\\hline\r\n&-8&+&38i&-&35(-1) \\\\\r\n+&35&&&\\Longleftarrow & \\\\\r\n\\hline\r\n&27&+&38i&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
    4. [latex]-32i+64i+4+12i[\/latex]\r\n[latex]-28+76i[\/latex]<\/li>\r\n \t
    5. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrl}\r\n&32&+&24i&& \\\\\r\n&&-&16i&-&12i^2 \\\\\r\n\\hline\r\n&32&+&8i&-&12(-1) \\\\\r\n+&12&&&\\Longleftarrow & \\\\\r\n\\hline\r\n&44&+&8i&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
    6. [latex]-18i+12i^2-28i^2[\/latex]\r\n[latex]-18i+12(-1)-28(-1)[\/latex]\r\n[latex]-18i-12+28[\/latex]\r\n[latex]-18i+16[\/latex]<\/li>\r\n \t
    7. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrl}\r\n&2&+&10i&& \\\\\r\n&&+&i&+&5i^2 \\\\\r\n\\hline\r\n&2&+&11i&+&5(-1) \\\\\r\n-&5&&&\\Longleftarrow & \\\\\r\n\\hline\r\n&-3&+&11i&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
    8. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrl}\r\n&-6&+&3i&& \\\\\r\n&&+&10i&-&5i^2 \\\\\r\n\\hline\r\n&-6&+&13i&-&5(-1) \\\\\r\n+&5&&&\\Longleftarrow & \\\\\r\n\\hline\r\n&-1&+&13i&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
    9. [latex]\\dfrac{-9+5i}{i}\\cdot \\dfrac{i}{i}\\Rightarrow \\dfrac{-9i+5i^2}{i^2}\\Rightarrow \\dfrac{-9i+5(-1)}{(-1)}\\Rightarrow 9i+5[\/latex]<\/li>\r\n \t
    10. [latex]\\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}[\/latex]<\/li>\r\n \t
    11. [latex]\\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}[\/latex]<\/li>\r\n \t
    12. [latex]\\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}[\/latex]<\/li>\r\n \t
    13. [latex]\\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}[\/latex]<\/li>\r\n \t
    14. [latex]\\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}[\/latex]<\/li>\r\n \t
    15. [latex]\\dfrac{10-i}{-i}\\cdot \\dfrac{i}{i}\\Rightarrow \\dfrac{10i-i^2}{-i^2}\\Rightarrow \\dfrac{10i-(-1)}{-(-1)}\\Rightarrow 10i+1[\/latex]<\/li>\r\n \t
    16. [latex]\\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[\/latex]<\/li>\r\n \t
    17. [latex]\\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}[\/latex]<\/li>\r\n \t
    18. [latex]\\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[\/latex]\r\n[latex]\\dfrac{9i-45}{26}[\/latex]<\/li>\r\n \t
    19. [latex]\\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}[\/latex]<\/li>\r\n \t
    20. [latex]\\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}[\/latex]<\/li>\r\n \t
    21. [latex]\\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}[\/latex]<\/li>\r\n \t
    22. [latex]\\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[\/latex]\r\n[latex]\\dfrac{-36+27i}{50}[\/latex]<\/li>\r\n \t
    23. [latex]\\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}[\/latex]<\/li>\r\n \t
    24. [latex]\\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}[\/latex]<\/li>\r\n \t
    25. [latex]\\pm 9i[\/latex]<\/li>\r\n \t
    26. [latex]\\sqrt{-5\\cdot 9}\\Rightarrow \\pm 3\\sqrt{5}i[\/latex]<\/li>\r\n \t
    27. [latex]\\sqrt{-20}\\Rightarrow \\sqrt{-4\\cdot 5}\\Rightarrow \\pm2\\sqrt{5}i[\/latex]<\/li>\r\n \t
    28. [latex]\\sqrt{24}\\Rightarrow \\sqrt{4\\cdot 6}\\Rightarrow \\pm 2\\sqrt{6}[\/latex]<\/li>\r\n \t
    29. [latex]\\dfrac{3+\\sqrt{3\\cdot -9}}{6}\\Rightarrow \\dfrac{3+3\\sqrt{3}i}{6}\\Rightarrow \\dfrac{1+\\sqrt{3}i}{2}[\/latex]<\/li>\r\n \t
    30. [latex]\\dfrac{-4-\\sqrt{-2\\cdot 4}}{-4}\\Rightarrow \\dfrac{-4-2\\sqrt{2}i}{-4}\\Rightarrow \\dfrac{2+\\sqrt{2}i}{2}[\/latex]<\/li>\r\n \t
    31. [latex]\\dfrac{8-4i}{4}\\Rightarrow 2-i[\/latex]<\/li>\r\n \t
    32. [latex]\\dfrac{6+\\sqrt{2\\cdot -16}}{4}\\Rightarrow \\dfrac{6+4\\sqrt{2}i}{4}\\Rightarrow \\dfrac{3+2\\sqrt{2}i}{2}[\/latex]<\/li>\r\n<\/ol>\r\n
        \r\n \t
      1. [latex]i[\/latex]<\/li>\r\n \t
      2. [latex]i^3\\Rightarrow -i[\/latex]<\/li>\r\n \t
      3. 1<\/li>\r\n \t
      4. 1<\/li>\r\n \t
      5. [latex]i^2\\Rightarrow -1[\/latex]<\/li>\r\n \t
      6. [latex]i[\/latex]<\/li>\r\n \t
      7. [latex]i^2\\Rightarrow -1[\/latex]<\/li>\r\n \t
      8. [latex]i^3\\Rightarrow -i[\/latex]<\/li>\r\n<\/ol>","rendered":"
          \n
        1. [latex]3+8-4i[\/latex]
          \n[latex]11-4i[\/latex]<\/li>\n
        2. [latex]3i-7i[\/latex]
          \n[latex]-4i[\/latex]<\/li>\n
        3. [latex]7i-3+2i[\/latex]
          \n[latex]9i-3[\/latex]<\/li>\n
        4. [latex]5-6-6i[\/latex]
          \n[latex]-1-6i[\/latex]<\/li>\n
        5. [latex]-6i-3-7i[\/latex]
          \n[latex]-13i-3[\/latex]<\/li>\n
        6. [latex]-8i-7i-5+3i[\/latex]
          \n[latex]-12i-5[\/latex]<\/li>\n
        7. [latex]3-3i-7-8i[\/latex]
          \n[latex]-4-11i[\/latex]<\/li>\n
        8. [latex]-4-i+1-5i[\/latex]
          \n[latex]-3-6i[\/latex]<\/li>\n
        9. [latex]i-2-3i-6[\/latex]
          \n[latex]-2i-8[\/latex]<\/li>\n
        10. [latex]5-4i+8-4i[\/latex]
          \n[latex]13-8i[\/latex]<\/li>\n
        11. [latex]-48i^2[\/latex]
          \n[latex]-48(-1)[\/latex]
          \n[latex]48[\/latex]<\/li>\n
        12. [latex]-24i^2[\/latex]
          \n[latex]-24(-1)[\/latex]
          \n[latex]24[\/latex]<\/li>\n
        13. [latex]-40i^2[\/latex]
          \n[latex]-40(-1)[\/latex]
          \n[latex]40[\/latex]<\/li>\n
        14. [latex]-32i^2[\/latex]
          \n[latex]-32(-1)[\/latex]
          \n[latex]32[\/latex]<\/li>\n
        15. [latex]49i^2[\/latex]
          \n[latex]49(-1)[\/latex]
          \n[latex]-49[\/latex]<\/li>\n
        16. [latex]-7i^2(4-3i)[\/latex]
          \n[latex]-28i^2+21i^3[\/latex]
          \n[latex]-28(-1)+21(-1)i[\/latex]
          \n[latex]28-21i[\/latex]<\/li>\n
        17. [latex]36+60i+25i^2[\/latex]
          \n[latex]36+60i+25(-1)[\/latex]
          \n[latex]36+60i-25[\/latex]
          \n[latex]11+60i[\/latex]<\/li>\n
        18. [latex]16i^2(-2-8i)[\/latex]
          \n[latex]32i^2+128i^3[\/latex]
          \n[latex]32(-1)+128(-1)i[\/latex]
          \n[latex]-32-128i[\/latex]<\/li>\n<\/ol>\n
            \n
          1. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrl} &56&-&42i&& \\\\ &&+&32i&-&24i^2 \\\\ \\hline &56&-&10i&-&24(-1) \\\\ +&24&&&\\Longleftarrow & \\\\ \\hline &80&-&10i&& \\end{array}[\/latex]<\/li>\n
          2. [latex]9i^2(4-4i)[\/latex]
            \n[latex]-36i^2+36i^3[\/latex]
            \n[latex]-36(-1)+36(-1)i[\/latex]
            \n[latex]36-36i[\/latex]<\/li>\n
          3. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrl} &-8&+&10i&& \\\\ &&+&28i&-&35i^2 \\\\ \\hline &-8&+&38i&-&35(-1) \\\\ +&35&&&\\Longleftarrow & \\\\ \\hline &27&+&38i&& \\end{array}[\/latex]<\/li>\n
          4. [latex]-32i+64i+4+12i[\/latex]
            \n[latex]-28+76i[\/latex]<\/li>\n
          5. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrl} &32&+&24i&& \\\\ &&-&16i&-&12i^2 \\\\ \\hline &32&+&8i&-&12(-1) \\\\ +&12&&&\\Longleftarrow & \\\\ \\hline &44&+&8i&& \\end{array}[\/latex]<\/li>\n
          6. [latex]-18i+12i^2-28i^2[\/latex]
            \n[latex]-18i+12(-1)-28(-1)[\/latex]
            \n[latex]-18i-12+28[\/latex]
            \n[latex]-18i+16[\/latex]<\/li>\n
          7. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrl} &2&+&10i&& \\\\ &&+&i&+&5i^2 \\\\ \\hline &2&+&11i&+&5(-1) \\\\ -&5&&&\\Longleftarrow & \\\\ \\hline &-3&+&11i&& \\end{array}[\/latex]<\/li>\n
          8. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrl} &-6&+&3i&& \\\\ &&+&10i&-&5i^2 \\\\ \\hline &-6&+&13i&-&5(-1) \\\\ +&5&&&\\Longleftarrow & \\\\ \\hline &-1&+&13i&& \\end{array}[\/latex]<\/li>\n
          9. [latex]\\dfrac{-9+5i}{i}\\cdot \\dfrac{i}{i}\\Rightarrow \\dfrac{-9i+5i^2}{i^2}\\Rightarrow \\dfrac{-9i+5(-1)}{(-1)}\\Rightarrow 9i+5[\/latex]<\/li>\n
          10. [latex]\\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}[\/latex]<\/li>\n
          11. [latex]\\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}[\/latex]<\/li>\n
          12. [latex]\\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}[\/latex]<\/li>\n
          13. [latex]\\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}[\/latex]<\/li>\n
          14. [latex]\\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}[\/latex]<\/li>\n
          15. [latex]\\dfrac{10-i}{-i}\\cdot \\dfrac{i}{i}\\Rightarrow \\dfrac{10i-i^2}{-i^2}\\Rightarrow \\dfrac{10i-(-1)}{-(-1)}\\Rightarrow 10i+1[\/latex]<\/li>\n
          16. [latex]\\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[\/latex]<\/li>\n
          17. [latex]\\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}[\/latex]<\/li>\n
          18. [latex]\\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[\/latex]
            \n[latex]\\dfrac{9i-45}{26}[\/latex]<\/li>\n
          19. [latex]\\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}[\/latex]<\/li>\n
          20. [latex]\\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}[\/latex]<\/li>\n
          21. [latex]\\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}[\/latex]<\/li>\n
          22. [latex]\\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[\/latex]
            \n[latex]\\dfrac{-36+27i}{50}[\/latex]<\/li>\n
          23. [latex]\\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}[\/latex]<\/li>\n
          24. [latex]\\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}[\/latex]<\/li>\n
          25. [latex]\\pm 9i[\/latex]<\/li>\n
          26. [latex]\\sqrt{-5\\cdot 9}\\Rightarrow \\pm 3\\sqrt{5}i[\/latex]<\/li>\n
          27. [latex]\\sqrt{-20}\\Rightarrow \\sqrt{-4\\cdot 5}\\Rightarrow \\pm2\\sqrt{5}i[\/latex]<\/li>\n
          28. [latex]\\sqrt{24}\\Rightarrow \\sqrt{4\\cdot 6}\\Rightarrow \\pm 2\\sqrt{6}[\/latex]<\/li>\n
          29. [latex]\\dfrac{3+\\sqrt{3\\cdot -9}}{6}\\Rightarrow \\dfrac{3+3\\sqrt{3}i}{6}\\Rightarrow \\dfrac{1+\\sqrt{3}i}{2}[\/latex]<\/li>\n
          30. [latex]\\dfrac{-4-\\sqrt{-2\\cdot 4}}{-4}\\Rightarrow \\dfrac{-4-2\\sqrt{2}i}{-4}\\Rightarrow \\dfrac{2+\\sqrt{2}i}{2}[\/latex]<\/li>\n
          31. [latex]\\dfrac{8-4i}{4}\\Rightarrow 2-i[\/latex]<\/li>\n
          32. [latex]\\dfrac{6+\\sqrt{2\\cdot -16}}{4}\\Rightarrow \\dfrac{6+4\\sqrt{2}i}{4}\\Rightarrow \\dfrac{3+2\\sqrt{2}i}{2}[\/latex]<\/li>\n<\/ol>\n
              \n
            1. [latex]i[\/latex]<\/li>\n
            2. [latex]i^3\\Rightarrow -i[\/latex]<\/li>\n
            3. 1<\/li>\n
            4. 1<\/li>\n
            5. [latex]i^2\\Rightarrow -1[\/latex]<\/li>\n
            6. [latex]i[\/latex]<\/li>\n
            7. [latex]i^2\\Rightarrow -1[\/latex]<\/li>\n
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