Complex Numbers Worksheet - Appendix F, Cengage Page 10
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11F10
APPENDIX F
Complex Numbers
EXAMPLE 10
Finding the nth Roots of a Complex Number
Find the three cube roots of
z
2
2i.
Solution
Because z lies in Quadrant II, the polar form for z is
z
2
2i
8 cos 135
i sin 135 .
By the formula for nth roots, the cube roots have the form
135
360 k
135
360 k
6
8 cos
i sin
.
3
3
Finally, for
k
0, 1,
and 2, you obtain the roots
2 cos 45
i sin 45
1
i
2 cos 165
i sin 165
1.3660
0.3660i
2 cos 285
i sin 285
0.3660
1.3660i.
E X E R C I S E S F O R A P P E N D I X F
In Exercises 1–24, perform the operation and write the result in
In Exercises 25–32, write the complex conjugate of the complex
standard form.
number. Then multiply the number by its complex conjugate.
1.
5
i
6
2i
25.
5
3i
26.
9
12i
2.
13
2i
5
6i
27.
2
5i
28.
4
2i
3.
8
i
4
i
29.
20i
30.
15
4.
3
2i
6
13i
31.
8
32.
1
8
5.
2
8
5
50
In Exercises 33–42, write the quotient in standard form.
6.
8
18
4
3 2i
6
10
7.
13i
14
7i
33.
34.
i
2i
8.
22
5
8i
10i
4
3
3
5
5
11
35.
36.
9.
i
i
2
2
3
3
4
5i
1
i
10.
1.6
3.2i
5.8
4.3i
2
i
8
7i
37.
38.
11.
6
2
2
i
1
2i
12.
5
10
6
7i
8
20i
39.
40.
2
10
13.
i
2i
2
14.
75
1
2
3i 5i
41.
42.
15.
1
i 3
2i
2
4
5i
2
3i
16.
6
2i 2
3i
17.
6i 5
2i
In Exercises 43–46, perform the operation and write the result
in standard form.
18.
8i 9
4i
19.
14
10i
14
10i
2
3
2i
5
43.
44.
20.
3
5 7
10
1
i
1
i
2
i
2
i
2
21.
4
5i
i
2i
1
i
3
2
45.
46.
22.
2
3i
3
2i
3
8i
i
4
i
2
2
23.
2
3i
2
3i
2
2
24.
1
2i
1
2i
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education