# Honors Algebra 2: Extra Practice with Operations on Complex Numbers

• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown

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Simplify Completely:

1. $$\displaystyle 6i \cdot 7i$$
2. Solution

-42

3. $$\displaystyle -i \sqrt{3} \cdot i \sqrt{5}$$
4. Solution

$$\displaystyle \sqrt{15}$$

5. $$\displaystyle i \sqrt{3} \cdot i \sqrt{2} \cdot i \sqrt{6}$$
6. Solution

$$\displaystyle -6i$$

7. $$\displaystyle \sqrt{-5} \cdot \sqrt{-6}$$
8. Solution

$$\displaystyle -\sqrt{30}$$

9. $$\displaystyle -3 \sqrt{-2} \cdot 4 \sqrt{-11}$$
10. Solution

$$\displaystyle 12\sqrt{22}$$

11. $$\displaystyle 2 \sqrt{3} \cdot 3 \sqrt{-2}$$
12. Solution

$$\displaystyle 6i\sqrt{6}$$

13. $$\displaystyle (4 + 3i)(5 + 6i)$$
14. Solution

$$\displaystyle 2 + 39i$$

15. $$\displaystyle (3 - 4i)(2 + 2i)$$
16. Solution

$$\displaystyle 14 - 2i$$

17. $$\displaystyle (-7 - 6i)(-7 + 6i)$$
18. Solution

85

19. $$\displaystyle (6 - 2i)^2$$
20. Solution

$$\displaystyle 32 - 24i$$

21. $$\displaystyle (-5 - i)^2$$
22. Solution

$$\displaystyle 24 + 10i$$

23. $$\displaystyle (-4i)^3$$
24. Solution

$$\displaystyle 64i$$

25. $$\displaystyle \left( i \sqrt{3} \right)^4$$
26. Solution

9

27. $$\displaystyle (-2i)^5$$
28. Solution

$$\displaystyle -32i$$

29. $$\displaystyle \frac{7}{i}$$
30. Solution

$$\displaystyle -7i$$

31. $$\displaystyle -\frac{8}{12i}$$
32. Solution

$$\displaystyle \frac{2}{3}i$$

33. $$\displaystyle \frac{5}{3 + 2i}$$
34. Solution

$$\displaystyle \frac{15}{13} - \frac{10}{13}i$$

35. $$\displaystyle -\frac{3}{4 - 2i}$$
36. Solution

$$\displaystyle -\frac{3}{5} - \frac{3}{10}i$$

37. $$\displaystyle \frac{i}{-1 + i}$$
38. Solution

$$\displaystyle \frac{1}{2} - \frac{1}{2}i$$

39. $$\displaystyle \frac{5i}{-3 - i}$$
40. Solution

$$\displaystyle - \frac{1}{2} - \frac{3}{2}i$$

41. $$\displaystyle \frac{2 + 3i}{3 - 4i}$$
42. Solution

$$\displaystyle -\frac{6}{25} + \frac{17}{25}i$$

43. $$\displaystyle \frac{5 - 3i}{1 - i}$$
44. Solution

$$\displaystyle 4 + i$$

45. $$\displaystyle \frac{1 - 3i}{-2 - 4i}$$
46. Solution

$$\displaystyle \frac{1}{2} + \frac{1}{2}i$$

47. $$\displaystyle \frac{50}{3 \sqrt{5} + \sqrt{-5}}$$
48. Solution

$$\displaystyle 3\sqrt{5} - i\sqrt{5}$$

49. $$\displaystyle (-2i)^8$$
50. Solution

256

51. $$\displaystyle i^{11}$$
52. Solution

$$\displaystyle -i$$