NEW
Font size
S
M
L
XL
WorksheetsComplex Numbers and the Polar Coordinate Plane
Total questions: 10
Worksheet time: 1hrs 10mins
Name
Class
Date
1.
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
2.
Find the modulus of the complex number. Also state what quadrant the point would land in.
-3 + i
a)
√10, Quadrant 2
b)
√10, Quadrant 3
c)
2, Quadrant 2
d)
3, Quadrant 3
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.
What class are you in?
a)
Precalculus
b)
Algebra 2
c)
Algebra 1
d)
P.E
5.
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)
6.
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
7.
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
8.
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
9.
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
10.
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
Reset
