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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

Some say that Euler's identity (e^(i*pi)+1=0) is so mysterious that it can hardly be comprehended.
true

Some say that Euler's identity (e^(i*pi)+1=0) is so mysterious that it can hardly be comprehended.
true

AC voltage of 5*exp(0.927i) has an phase of
0.927 radians

AC voltage of 5*exp(i53.13 deg) has an amplitude of
5 volts

sin(z), cos(z), tan(z), ln(z), log(z) are defined when z is a complex number
true

exp(i*z) is the same as
cos(z)+i*sin(z), which is know as Euler's formula

Complex numbers can be
A) added and subtracted
B) multiplied and divided
C) placed in matrices
D) all of these
D) all of these (this multiple choice question has been scrambled)

The sum of 3 and i4 has an angle of
A) 0.927 radians
B) both of these
C) both of these
D) 53.13 degrees
B) both of these (this multiple choice question has been scrambled)

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

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

exp(i*pi)*2=e^(i*pi)*2 is a complex number in polar form and is also
2i
2
2
2i
2

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

exp(1)=e^(1) is known as Euler's number and is
2.71828

The angle (radians) of the sum of 3 and i4 is
3+i4
7
5
0.9273
0.9273

The magnitude of the sum of 3 and i4 is
7
5
3+i4
sqrt(3^2+(4i)^2)
5

The sum of 3 and 4i is
5
3+i4
sqrt(3^2+4^2)
7
3+i4

The angle of 3+i4 is
53.13 deg
3
5
4
53.13 deg

The magnitude of 3+i4 is
53.13 deg
3
5
4
5

The imaginary part of 3+4i is
53.13 deg
5
3
4
4

The real part of 3+i4 is
3
5
i4
4
3

The number (3+i4) is an example of a _______ number in rectangular form.
imaginary
complex
real
polar
complex

Complex numbers
are frequently used in electrical engineering

A complex number is
like a 2D vector




The square root of 1 is
the symbol i (usually and in calculators) or the symbol j (in electrical engineering)

The augment function in the TI89
combines two vectors into a matrix

x/norm(x) sto> uu(x) is a TI89 function. Then typing: uu(A) will calculate the ______ of vectorA
unit vector in the direction

In calculating torqueT about pointO by T=crossP(R,F), the direction of T
perpendicular to both R and F and is given by the righthand rule

In calculating torque about pointO by crossP(R,F), R
vector from pointO to any point on the line of action of forceF

The formula for calculating torque is
R cross F = crossP(R,F)

acos( dotP(a,b) / ( norm(a) * norm(b) ) ) sto> nn(a,b) is a TI89 function that computes the
angle between vectors a and b

In crossP(a,b) = c
c is perpendicular to both a and b

Regarding a,b,c in crossP(a,b) = c,
all are 3D vectors

The crossproduct operation is commutative which means crossP(a,b) = crossP(b,a)
false

The dotproduct operation is commutative which means dotP(a,b) = dotP(b,a)
true

. A 3D vector with components a,b, and c can stored into a column vector as
[a;b;c]

A 3D vector with components a,b, and c can be stored into a row vector as
[a,b,c]

The cross product of two 3D vectors is useful
in 3D torque problems

The cross product of two 3D vectors is
a 3D vector

The magnitude of the cross product of two vectors A and B is
norm(A)*norm(B)*sin(theta)

The length of a 3D vector A=[a,b,c] is norm(A)=
sqrt(a*a + b*b + c*c)

The dot product of two vectors A and B is defined as dotP(A,B)=
norm(A) * norm(B) * cos(theta)

The dot product is useful for calculating the angle between two vectors:
(2D or 3D)

The dot product of two 3D vectors is
a scalar (not a vector), which is the same as a number

vector = [1.2, 3.4, 5.6], where 1.2 is called the _____ component
first

A vector that has a length of one is called a ______ vector.
unit

In the TI89, the magnitude of _______ can be determined by the _____ function.
a 2D or 3D mechanical vector, norm()

Orthogonal means
perpendicular to

Dot products and cross products are not defined for
complex numbers

Dot products are great for finding
angle between two vectors in 2D or 3D.

Dot products are defined for
mechanical vectors, but not for complex numbers

A vector with a magnitude of one is called ______ vector.
a unit

. When a vector is multiplied by a scalar, the scalar is multiplied by
each vector component or the vector magnitude

A complex number that has an angle of zero is called
a scalar

Mechanical vectors and complex numbers can be added and subtracted
true

A complex number of magnitude 5 and angle 53.13 degrees
(3+3i)
(3+4i)
(4+4i)
(4+3i)
(3+4i)

In the TI89, the complex number with an xcomponent of 3 and ycomponent of 4 is ______, where "/_" is the "angle" symbol, common in the TI89.
(5 /_ 53.13 deg )
[5 + /_ 53.13 deg ]
(5 + /_ 53.13 deg )
5 /_ 53.13 deg
(5 /_ 53.13 deg )

In the TI89, the complex number with an xcomponent of 2 and ycomponent of 3
[2+3]
[2,3]
(2,3i)
(2+3i)
(2+3i)

In the TI89, the mechanical vector with an xcomponent of 2 and ycomponent of 3
(2+3i)
[2+3]
(2,3i)
[2,3]
[2,3]

TI89 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

In the TI89, mechanical vectors are placed in ____ separated by commas.
brackets

Given x and y components of a vector in the first quadrant, the angle is
atan(y/x)

Given x and y components of a vector in the first quadrant, the magnitude is
sqrt( x^2 + y^2)

Given a vector (Mangletheta)=(M/_theta), where theta is in the first quadrant, the vertical component is
M*sin(theta)

Given a vector (Mangletheta) in the first quadrant, the horizontal component is
M*cos(theta)

The manual way to add two vectors is to
add horizontal components and add vertical components

Two vectors are added by placing the tail of the
second vector at the head of the first vector.

Length of a vector and direction of a vector are identified as
magnitude and angle

. i in a complex number identifies the _____ of the complex number.
vertical component

Complex numbers are the same as 2D _____ vectors
mechanical

A complex number (electrical vector) can be resolved into horizontal and vertical components called
real and imaginary parts

A mechanical vector can be resolved into horizontal and vertical parts called
x and y components

A vector has
magnitude and direction

TI89 angles are measured
positive when counterclockwise from xaxis

Airplane angles are
always positive

An airplane angle of ____ is the same as 100 degrees.
N10W or 10 degrees NW

Airplane angles are measured from
North or South

The maximum airplane angle is _____ degrees
90

A vector with an angle of negativepi/2 radians point along the _____ axis
y

A vector with an angle of negativepi radians point along the _____ axis
x

A vector with an angle of pi radians point along the _____ axis
x

A vector with an angle of pi/2 radians point along the _____ axis
+y

Positive angles "go" _______ from the ________.
counterclockwise, xaxis

Angles are measured relative to the
positive x axis

The number of gradians in 360 degrees is
400

The dimension of a radian is
dimensionless  a radian has no dimensions

An angle of one radian occurs when the _____ and the arc length are ____.
radius, the same

The angle measured in radians is
the arc length divided by the radius

The number of degrees in one radian is approximately
57

The number of radians in 180 degrees is
pi

The matrix method in solving simulaneously linear equations is most efficient because
the unknown variables, x and y, are not entered into the calculator

