WorksheetsMultiple Divide Complex Numbers Polar Form
Total questions: 27
Worksheet time: 3hrs 24mins
Name
Class
Date
1.
Find the modulus or absolute value of the complex number. Also state what quadrant the point would land in graphically.
-3 + i
a)
√10, Quadrant 2
b)
√10, Quadrant 3
c)
2, Quadrant 2
d)
3, Quadrant 3
2.
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
3.
Express the complex number in polar form.
-2 + 5i
-2 + 5i
a)
5.39 ( cos 1.95 + i sin 1.95)
b)
5.39 ( cos 65.06 + i sin 65.06)
c)
2.65 ( cos 1.95 - i sin 1.95 )
d)
2.65 ( cos 65. 06 - i sin 65.06 )
4.
Which are possible coordinates of the point graphed?
a)
(-2, 120o)
b)
(-2, 60o)
c)
(2, -120o)
d)
(2, 60o)
5.
What complex number is represented by the graph?
a)
-3-i
b)
-3+i
c)
1+3i
d)
1-3i
6.
Convert the rectangular coordinate (0, -3) to polar coordinates.
a)
(3, -270o)
b)
(3, 270o)
c)
(-3, 270o)
d)
Not Possible
7.
Express the complex number in polar form.
6 + 2i
6 + 2i
a)
6.32 ( cos 0.32 + i sin 0.32)
b)
6.32 ( cos 0.45 + i sin 0.45)
c)
1.73 ( cos 0.32 + i sin 0.32)
d)
1.73 ( cos 0.45 - i sin 0.45)
8.
What quadrant would the point in polar form land in?
4 ( cos π /3 + i sin π /3)
4 ( cos π /3 + i sin π /3)
a)
Quadrant 4
b)
Quadrant 1
c)
Quadrant 2
d)
Quadrant 3
9.
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
10.
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
11.
Find
(3 + 3√3 i )4
using De Moivre's Theorem and express your answer in rectangular form.
(3 + 3√3 i )4
using De Moivre's Theorem and express your answer in rectangular form.
a)
-648 - 648 √3 i
b)
-654 - 654 √3 i
c)
-1962 - 1962 √3 i
d)
648 i
12.
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)
13.
Find the product z₁z₂
a)
-7√3 - 7i
b)
-7√2 - 7√2i
c)
-7√2 + 7√2i
d)
-7 - 7√3i
14.
Find the quotient z₁ ⁄ z₂
a)
-3.5 + i
b)
-3.5i
c)
-3.5
d)
3.5
15.
Find the product z₁z₂
a)
15 - 15i
b)
-15
c)
-15i
d)
15i
16.
Find the quotient z₁ ⁄ z₂
a)
-3√3/10 + 3/10
b)
3√3/2 - 3/2
c)
3√3/10 + 3/10
d)
3√3/5 - 3/5
17.
Find the indicated power using DeMoivre's Theorem
a)
256
b)
4096i
c)
4096
d)
-4096
18.
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
19.
Convert (1 + √3i) to Polar (cis) Form.
a)
2 cis(π/6)
b)
2 cis(π/3)
c)
4 cis(π/6)
d)
4 cis(π/3)
20.
If z = 2(cos(20) + isin(20)) and w = 3(cos(105) + isin(105)), find z / w
a)
2/3(cos(-85) + isin(-85))
b)
2/3(cos(275) + isin(275))
c)
3/2(cos(85) + isin(85))
d)
6(cos(125) + isin(125))
21.
If z = 2(cos(120) + isin(120)) and w = 3(cos(305) + isin(305)), find z ⋅ w
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))
22.
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)
23.
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
24.
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
25.
Find the absolute value of the complex number. Also state what quadrant the point would land in.
2 + 3i
2 + 3i
a)
√13, Quadrant 1
b)
√5, Quadrant 1
c)
√11, Quadrant 2
d)
√11, Quadrant 3
26.
Convert (-√2 - √2i) to Polar (cis) Form.
a)
4 cis(π/4)
b)
2 cis(π/4)
c)
4 cis(5π/4)
d)
2 cis(5π/4)
27.
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)
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