Solutions 12: Complex Numbers

Solutions to Try Its

1. [latex]\sqrt{-24}=0+2i\sqrt{6}[/latex]

2.
Graph of the plotted point, -4-i.

3. [latex]\left(3 - 4i\right)-\left(2+5i\right)=1 - 9i[/latex]

4. [latex]-8 - 24i[/latex]

5. [latex]18+i[/latex]

6. [latex]102 - 29i[/latex]

7. [latex]-\frac{3}{17}+\frac{5i}{17}[/latex]

Solution to Odd-Numbered Exercises

1. Add the real parts together and the imaginary parts together.

3. i times i equals –1, which is not imaginary. (answers vary)

5. [latex]-8+2i[/latex]

7. [latex]14+7i[/latex]

9. [latex]-\frac{23}{29}+\frac{15}{29}i[/latex]

11. 2 real and 0 nonreal

13.
Graph of the plotted point, 1-2i.

15.
Graph of the plotted point, i.

17. [latex]8-i[/latex]

19. [latex]-11+4i[/latex]

21. [latex]2 - 5i[/latex]

23. [latex]6+15i[/latex]

25. [latex]-16+32i[/latex]

27. [latex]-4 - 7i[/latex]

29. 25

31. [latex]2-\frac{2}{3}i[/latex]

33. [latex]4 - 6i[/latex]

35. [latex]\frac{2}{5}+\frac{11}{5}i[/latex]

37. 15i

39. [latex]1+i\sqrt{3}[/latex]

41. 1

43. –1

45. 128i

47. [latex]{\left(\frac{\sqrt{3}}{2}+\frac{1}{2}i\right)}^{6}=-1[/latex]

49. 3i

51. 0

53. 5 – 5i

55. –2i

57. [latex]\frac{9}{2}-\frac{9}{2}i[/latex]