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WorksheetsVectors and Trig Form of Complex Numbers
Total questions: 20
Worksheet time: 2hrs 53mins
Name
Class
Date
1.
Find the magnitude of the vector <2, -3>.
a)
√11
b)
13
c)
√-4
d)
√13
2.
Find the direction of the vector <-3, -5>.
a)
59.03°
b)
239.03°
c)
210.96°
d)
120.96°
3.
Find the dot product of <1, -2> and <3, 2>.
a)
1
b)
<3, -4>
c)
<4, 0>
d)
-1
4.
Find the angle between vectors <1,3> and <2,-5>.
a)
40.24°
b)
49.76°
c)
139.76°
d)
92.57°
5.
How do you know if two vectors are orthogonal?
a)
Their sum is 0.
b)
The dot product is 1.
c)
The angle between them is 0°.
d)
The dot product is 0.
6.
Find the angle between u and v.
a)
78.930o
b)
33.691o
c)
101.070o
d)
146.310o
7.
Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS.
a)
〈14,-13〉
b)
〈-14,13〉
c)
〈-40,-21〉
d)
〈40,-21〉
8.
Determine the direction and magnitude of the vector 〈-11,5〉
a)
Direction 24.4°
Vertical 12.1
Vertical 12.1
b)
Direction65.6°
Magnitude 12.1
Magnitude 12.1
c)
Direction -24.4°
Magnitude 12.1
Magnitude 12.1
d)
Direction 155.6°
Magnitude 12.1
Magnitude 12.1
9.
Given u = <3, 7> and v =<-5, 4>, find 2v - 3u
a)
<21, 2>
b)
<-19, -13>
c)
<-15, 3>
d)
23
10.
Write the complex number in polar form
a)
√50 (cos π/2 + i sin π/2)
b)
50 (cos π/4 + i sin π/4)
c)
√50 (cos 5π/4 + i sin 5π/4)
d)
√50 (cos π/4 + i sin π/4)
11.
Find the indicated power using DeMoivre's Theorem
a)
72 - 72√3i
b)
- 72√3 + 72i
c)
- 72√2 + 72√2i
d)
-72 + 72√3i
12.
Find the square roots of 4√3 + 4i
a)
2.705 + .725i and - 2.705 - .725i
b)
- 2.705 + .725i and 2.705 - .725i
c)
2.799 + .0128i and - 2.799 - .0128i
d)
- 2.799 + .0128i and 2.799 - .0128i
13.
Express the point in polar form in rectangular form.
4 ( cos π /3 + i sin π /3)
4 ( cos π /3 + i sin π /3)
a)
2 + 2√3 i
b)
2 + √3 i
c)
2 - 2√3 i
d)
-2 + 2√3 i
14.
Convert the rectangular coordinates to polar form
a)
(√8 , 7π/6)
b)
(4 , 3π/4)
c)
(√8 , π/6)
d)
(8 , 7π/6)
15.
Find
5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)
in polar form. Then express your final answer in rectangular form.
5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)
in polar form. Then express your final answer in rectangular form.
a)
-10
b)
10
c)
-10i
d)
10i
16.
Find
1/2 ( cos π /3 + i sin π /3)
÷ 3 ( cos π /6 + i sin π /6)
and express your final answer in rectangular form.
1/2 ( cos π /3 + i sin π /3)
÷ 3 ( cos π /6 + i sin π /6)
and express your final answer in rectangular form.
a)
√3/12 + 1/12 i
b)
12√3 + 12 i
c)
√3/12 - 1/12 i
d)
12√3 - 12i
17.
If z = 2(cos(120) + isin(120)) and w = 3(cos(305) + isin(305)), find z ⋅ w. Choose all that apply.
a)
3/2(cos(425) + isin(425))
b)
3/2(cos(125) + isin(125))
c)
6(cos(425) + isin(425))
d)
6(cos(65) + isin(65))
18.
Write the complex number in polar form
a)
3 ( cos 3π/2 + i sin 3π/2)
b)
3 ( cos π/2 + i sin π/2)
c)
9 ( cos 3π/2 + i sin 3π/2)
d)
3 ( cos 2π + i 2π)
19.
Convert 5√3 - 5i to Polar (cis) Form.
a)
√40 cis(11π/6)
b)
10 cis(π/6)
c)
10 cis(11π/6)
d)
√40 cis(-π/6)
20.
Find the square roots of 1 + i
a)
- 1.09 + .452i and 1.09 - .452i
b)
1.84 + .765i and -1.84 - .765i
c)
1.09 + .452i and -1.09 - .452i
d)
-1.84 + .765i and 1.84 - .765i
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