Complex Numbers Worksheet - Appendix F, Cengage Page 11
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APPENDIX F
Complex Numbers
In Exercises 47–54, use the Quadratic Formula to solve the
In Exercises 83–86, perform the operation and leave the result
quadratic equation.
in polar form.
2
47.
x
2x
2
0
83.
3 cos
i sin
4 cos
i sin
3
3
6
6
2
48.
x
6x
10
0
3
2
49.
4x
16x
17
0
84.
cos
i sin
6 cos
i sin
2
2
2
4
4
2
50.
9x
6x
37
0
5
2
85.
cos 140
i sin 140
cos 60
i sin 60
2
51.
4x
16x
15
0
3
3
cos 5
3
i sin 5
3
2
52.
9x
6x
35
0
86.
cos
i sin
2
53.
16t
4t
3
0
2
54.
5s
6s
3
0
In Exercises 87–94, use DeMoivre’s Theorem to find the indi-
cated power of the complex number. Write the result in stan-
In Exercises 55–62, simplify the complex number and write it in
dard form.
standard form.
5
87.
1
i
3
2
55.
6i
i
6
88.
2
2i
2
3
56.
4i
2i
10
89.
1
i
5
57.
5i
12
90.
1
i
3
58.
i
7
91.
2
3
i
3
59.
75
3
92.
4 1
3i
6
60.
2
5
5
10
93.
cos
i sin
1
4
4
61.
3
i
8
94.
2 cos
i sin
1
2
2
62.
3
2i
In Exercises 95–100, (a) use Theorem F.2 on page F9 to find the
In Exercises 63–68, plot the complex number and find its
indicated roots of the complex number, (b) represent each of
absolute value.
the roots graphically, and (c) write each of the roots in
standard form.
63.
5i
64.
5
65.
4
4i
66.
5
12i
95. Square roots of
5 cos 120
i sin 120
67.
6
7i
68.
8
3i
96. Square roots of
16 cos 60
i sin 60
4
4
97. Fourth roots of
16 cos
i sin
In Exercises 69–76, represent the complex number graphically,
3
3
and find the polar form of the number.
5
5
98. Fifth roots of
32 cos
i sin
69.
3
3i
70.
2
2i
6
6
71.
3
i
72.
1
3i
125
99. Cube roots of
1
3i
5
2
73.
2 1
3i
74.
3
i
2
100. Cube roots of
4 2 1
i
75.
6i
76.
4
In Exercises 77–82, represent the complex number graphically,
In Exercises 101–108, use Theorem F.2 on page F9 to find
and find the standard form of the number.
all the solutions of the equation and represent the solutions
graphically.
77.
2 cos 150
i sin 150
4
3
101.
x
i
0
102.
x
1
0
78.
5 cos 135
i sin 135
5
4
103.
x
243
0
104.
x
81
0
3
79.
cos 300
i sin 300
2
3
6
105.
x
64i
0
106.
x
64i
0
3
80.
cos 315
i sin 315
4
3
4
107.
x
1
i
0
108. x
1
i
0
3
3
81.
3.75 cos
i sin
4
4
82.
8 cos
i sin
12
12
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