Honors Algebra 2: Extra Practice with Operations on Complex Numbers

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Simplify Completely:

  1. \( \displaystyle 6i \cdot 7i\)
    2. Solution

    -42

  2. \( \displaystyle -i \sqrt{3} \cdot i \sqrt{5}\)
    3. Solution

    \( \displaystyle \sqrt{15} \)

  3. \( \displaystyle i \sqrt{3} \cdot i \sqrt{2} \cdot i \sqrt{6}\)
    4. Solution

    \( \displaystyle -6i \)

  4. \( \displaystyle \sqrt{-5} \cdot \sqrt{-6}\)
    5. Solution

    \( \displaystyle -\sqrt{30} \)

  5. \( \displaystyle -3 \sqrt{-2} \cdot 4 \sqrt{-11}\)
    6. Solution

    \( \displaystyle 12\sqrt{22} \)

  6. \( \displaystyle 2 \sqrt{3} \cdot 3 \sqrt{-2}\)
    7. Solution

    \( \displaystyle 6i\sqrt{6} \)

  7. \( \displaystyle (4 + 3i)(5 + 6i)\)
    8. Solution

    \( \displaystyle 2 + 39i \)

  8. \( \displaystyle (3 - 4i)(2 + 2i)\)
    9. Solution

    \( \displaystyle 14 - 2i \)

  9. \( \displaystyle (-7 - 6i)(-7 + 6i)\)
    10. Solution

    85

  10. \( \displaystyle (6 - 2i)^2\)
    11. Solution

    \( \displaystyle 32 - 24i \)

  11. \( \displaystyle (-5 - i)^2\)
    12. Solution

    \( \displaystyle 24 + 10i \)

  12. \( \displaystyle (-4i)^3\)
    13. Solution

    \( \displaystyle 64i \)

  13. \( \displaystyle \left( i \sqrt{3} \right)^4 \)
    14. Solution

    9

  14. \( \displaystyle (-2i)^5\)
    15. Solution

    \( \displaystyle -32i \)

  15. \( \displaystyle \frac{7}{i}\)
    16. Solution

    \( \displaystyle -7i \)

  16. \( \displaystyle -\frac{8}{12i}\)
    17. Solution

    \( \displaystyle \frac{2}{3}i \)

  17. \( \displaystyle \frac{5}{3 + 2i}\)
    18. Solution

    \( \displaystyle \frac{15}{13} - \frac{10}{13}i \)

  18. \( \displaystyle -\frac{3}{4 - 2i}\)
    19. Solution

    \( \displaystyle -\frac{3}{5} - \frac{3}{10}i \)

  19. \( \displaystyle \frac{i}{-1 + i}\)
    20. Solution

    \( \displaystyle \frac{1}{2} - \frac{1}{2}i \)

  20. \( \displaystyle \frac{5i}{-3 - i}\)
    21. Solution

    \( \displaystyle - \frac{1}{2} - \frac{3}{2}i \)

  21. \( \displaystyle \frac{2 + 3i}{3 - 4i}\)
    22. Solution

    \( \displaystyle -\frac{6}{25} + \frac{17}{25}i \)

  22. \( \displaystyle \frac{5 - 3i}{1 - i}\)
    23. Solution

    \( \displaystyle 4 + i \)

  23. \( \displaystyle \frac{1 - 3i}{-2 - 4i}\)
    24. Solution

    \( \displaystyle \frac{1}{2} + \frac{1}{2}i \)

  24. \( \displaystyle \frac{50}{3 \sqrt{5} + \sqrt{-5}}\)
    25. Solution

    \( \displaystyle 3\sqrt{5} - i\sqrt{5} \)

  25. \( \displaystyle (-2i)^8\)
    26. Solution

    256

  26. \( \displaystyle i^{11}\)
    27. Solution

    \( \displaystyle -i \)