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Unit 1

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Unit 2

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Unit 3

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Unit 4

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Unit 5

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Unit 6

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Unit 7

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Quiz

Lesson 1 Quiz: Complex Numbers in Trigonometric and Exponential Form and De Moivres Theorem

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  • Questions count: 20
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1.
STEM Vector Algebra Problem 1: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
-8
-4
10
6
2.
STEM Solid Geometry Problem 8: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
3.
STEM Solid Geometry Problem 5: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
4.
STEM Vector Algebra Problem 34: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
10
-4
-8
5.
STEM Solid Geometry Problem 38: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
6.
STEM Solid Geometry Problem 39: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
7.
STEM Solid Geometry Problem 14: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
8.
STEM Vector Algebra Problem 10: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
-4
-8
10
9.
STEM Vector Algebra Problem 14: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
-4
-8
10
10.
STEM Solid Geometry Problem 18: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
11.
STEM Solid Geometry Problem 11: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
12.
STEM Solid Geometry Problem 4: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
x2 + y2 + z2 - 4x + 2y - 6z = 25
13.
STEM Vector Algebra Problem 35: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
10
-4
-8
14.
If the tangent to y = x2 - 4x + 5 is parallel to the x-axis, the point of tangency is:
(2, 0)
(2, 1)
(4, 5)
(0, 5)
15.
STEM Vector Algebra Problem 6: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
10
-4
-8
6
16.
STEM Solid Geometry Problem 23: What is the equation of a sphere in 3D Cartesian coordinates with center C(2, -1, 3) and radius r = 5?
(x - 2)2 + (y + 1)2 + (z - 3)2 = 25
(x - 2)2 + (y - 1)2 + (z - 3)2 = 5
x2 + y2 + z2 - 4x + 2y - 6z = 25
(x + 2)2 + (y - 1)2 + (z + 3)2 = 25
17.
The vector product \(\vec{A} \times \vec{B}\) geometrically represents:
D) The scalar projection of $vec{A}$ on $vec{B}$
A) The angle between the two vectors
B) A vector perpendicular to both $vec{A}$ and $vec{B}$ with magnitude equal to the area of the spanned parallelogram
C) The work done by vector $vec{A}$ along $vec{B}$
18.
STEM Vector Algebra Problem 8: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
10
-4
-8
19.
STEM Vector Algebra Problem 5: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
-4
-8
10
20.
STEM Vector Algebra Problem 22: If vector A = (2, -3, 1) and vector B = (1, 2, -4), calculate the dot product A · B.
6
-4
-8
10
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