# ENT 300 exam I redo

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1. Engineering technology students know that Euler's identity (e^(i*pi)+1=0) is easy to understand, because e^(i*pi) is a complex number in polar form and is equal to -1.
true
2. Some say that Euler's identity (e^(i*pi)+1=0) is so mysterious that it can hardly be comprehended.
true
3. Some say that Euler's identity (e^(i*pi)+1=0) is so mysterious that it can hardly be comprehended.
true
4. AC voltage of 5*exp(0.927i) has an phase of
5. AC voltage of 5*exp(i53.13 deg) has an amplitude of
5 volts
6. sin(z), cos(z), tan(z), ln(z), log(z) are defined when z is a complex number
true
7. exp(i*z) is the same as
cos(z)+i*sin(z), which is know as Euler's formula
8. Complex numbers can be

B) multiplied and divided
C) placed in matrices
D) all of these
D) all of these
(this multiple choice question has been scrambled)
9. The sum of 3 and i4 has an angle of

B) both of these
C) both of these
D) 53.13 degrees
B) both of these
(this multiple choice question has been scrambled)
10. The sum of 3 and 4i is
exp(0.927i)*5
5*exp(0.927i)
both of these
• exp(0.927i)*5
• 5*exp(0.927i)
• both of these
11. exp(-i*pi/2)*3=e^(-i*pi/2)*3 is a complex number in polar form and is also
3
-3i
3i
-3
-3i
12. exp(-i*pi)*2=e^(-i*pi)*2 is a complex number in polar form and is also
2i
2
-2
-2i
-2
13. exp(i*pi)*1=e^(i*pi)*1 is a complex number in polar form and is the same as
1
-1
-i
i
-1
14. exp(1)=e^(1) is known as Euler's number and is
2.71828
15. The angle (radians) of the sum of 3 and i4 is

3+i4
7
5
0.9273
0.9273
16. The magnitude of the sum of 3 and i4 is
7
5
3+i4
sqrt(3^2+(4i)^2)
5
17. The sum of 3 and 4i is
5
3+i4
sqrt(3^2+4^2)
7
3+i4
18. The angle of 3+i4 is
53.13 deg
3
5
4
53.13 deg
19. The magnitude of 3+i4 is
53.13 deg
3
5
4
5
20. The imaginary part of 3+4i is
53.13 deg
5
3
4
4
21. The real part of 3+i4 is
3
5
i4
4
3
22. The number (3+i4) is an example of a _______ number in rectangular form.
imaginary
complex
real
polar
complex
23. Complex numbers
are frequently used in electrical engineering
24. A complex number is
like a 2D vector
25. i^4 is
-1
1
-i
i
1
26. i^3 is
i
-i
1
-1
-i
27. i*i is
j
-1
i
1
-1
28. The square root of -1 is
the symbol i (usually and in calculators) or the symbol j (in electrical engineering)
29. The augment function in the TI-89
combines two vectors into a matrix
30. x/norm(x) sto--> uu(x) is a TI-89 function. Then typing: uu(A) will calculate the ______ of vector-A
unit vector in the direction
31. In calculating torque-T about point-O by T=crossP(R,F), the direction of T
perpendicular to both R and F and is given by the right-hand rule
32. In calculating torque about point-O by crossP(R,F), R
vector from point-O to any point on the line of action of force-F
33. The formula for calculating torque is
R cross F = crossP(R,F)
34. acos( dotP(a,b) / ( norm(a) * norm(b) ) ) sto-> nn(a,b) is a TI-89 function that computes the
angle between vectors a and b
35. In crossP(a,b) = c
c is perpendicular to both a and b
36. Regarding a,b,c in crossP(a,b) = c,
all are 3D vectors
37. The cross-product operation is commutative which means crossP(a,b) = crossP(b,a)
false
38. The dot-product operation is commutative which means dotP(a,b) = dotP(b,a)
true
39. . A 3D vector with components a,b, and c can stored into a column vector as
[a;b;c]
40. A 3D vector with components a,b, and c can be stored into a row vector as
[a,b,c]
41. The cross product of two 3D vectors is useful
in 3D torque problems
42. The cross product of two 3D vectors is
a 3D vector
43. The magnitude of the cross product of two vectors A and B is
norm(A)*norm(B)*sin(theta)
44. The length of a 3D vector A=[a,b,c] is norm(A)=
sqrt(a*a + b*b + c*c)
45. The dot product of two vectors A and B is defined as dotP(A,B)=
norm(A) * norm(B) * cos(theta)
46. The dot product is useful for calculating the angle between two vectors:
(2D or 3D)
47. The dot product of two 3D vectors is
a scalar (not a vector), which is the same as a number
48. vector = [1.2, 3.4, 5.6], where 1.2 is called the _____ component
first
49. A vector that has a length of one is called a ______ vector.
unit
50. In the TI-89, the magnitude of _______ can be determined by the _____ function.
a 2D or 3D mechanical vector, norm()
51. Orthogonal means
perpendicular to
52. Dot products and cross products are not defined for
complex numbers
53. Dot products are great for finding
angle between two vectors in 2D or 3D.
54. Dot products are defined for
mechanical vectors, but not for complex numbers
55. A vector with a magnitude of one is called ______ vector.
a unit
56. . When a vector is multiplied by a scalar, the scalar is multiplied by
each vector component or the vector magnitude
57. A complex number that has an angle of zero is called
a scalar
58. Mechanical vectors and complex numbers can be added and subtracted
true
59. A complex number of magnitude 5 and angle 53.13 degrees
(3+3i)
(3+4i)
(4+4i)
(4+3i)
(3+4i)
60. In the TI-89, the complex number with an x-component of 3 and y-component of 4 is ______, where "/_" is the "angle" symbol, common in the TI-89.
(5 /_ 53.13 deg )
[5 + /_ 53.13 deg ]
(5 + /_ 53.13 deg )
5 /_ 53.13 deg
(5 /_ 53.13 deg )
61. In the TI-89, the complex number with an x-component of 2 and y-component of 3
[2+3]
[2,3]
(2,3i)
(2+3i)
(2+3i)
62. In the TI-89, the mechanical vector with an x-component of 2 and y-component of 3
(2+3i)
[2+3]
(2,3i)
[2,3]
[2,3]
63. TI-89 modes: radian and either rectangular or polar. Enter the complex number in polar form. "/_" is the angle symbol. The complex number is equivalent to (3+4i) = (5/_53.13 deg)
d= (5*e^(53.13*i))
b= ( 5*e^(i*53.13*pi/180) ) a= (5 /_ (53.13*pi/180) )
c= (5 /_ 53.13)
either a or b but not c or d
either a or b but not c or d
64. In the TI-89, mechanical vectors are placed in ____ separated by commas.
brackets
65. Given x and y components of a vector in the first quadrant, the angle is
atan(y/x)
66. Given x and y components of a vector in the first quadrant, the magnitude is
sqrt( x^2 + y^2)
67. Given a vector (M-angle-theta)=(M/_theta), where theta is in the first quadrant, the vertical component is
M*sin(theta)
68. Given a vector (M-angle-theta) in the first quadrant, the horizontal component is
M*cos(theta)
69. The manual way to add two vectors is to
70. Two vectors are added by placing the tail of the
second vector at the head of the first vector.
71. Length of a vector and direction of a vector are identified as
magnitude and angle
72. . i in a complex number identifies the _____ of the complex number.
vertical component
73. Complex numbers are the same as 2D _____ vectors
mechanical
74. A complex number (electrical vector) can be resolved into horizontal and vertical components called
real and imaginary parts
75. A mechanical vector can be resolved into horizontal and vertical parts called
x and y components
76. A vector has
magnitude and direction
77. TI-89 angles are measured
positive when counterclockwise from x-axis
78. Airplane angles are
always positive
79. An airplane angle of ____ is the same as 100 degrees.
N10W or 10 degrees NW
80. Airplane angles are measured from
North or South
81. The maximum airplane angle is _____ degrees
90
82. A vector with an angle of negative-pi/2 radians point along the _____ axis
-y
83. A vector with an angle of negative-pi radians point along the _____ axis
-x
84. A vector with an angle of pi radians point along the _____ axis
-x
85. A vector with an angle of pi/2 radians point along the _____ axis
+y
86. Positive angles "go" _______ from the ________.
counterclockwise, x-axis
87. Angles are measured relative to the
positive x axis
88. The number of gradians in 360 degrees is
400
89. The dimension of a radian is
dimensionless - a radian has no dimensions
90. An angle of one radian occurs when the _____ and the arc length are ____.