Force
A
, at 100 pounds, and force
B
,
at 120 pounds, make an angle of
with each other.
Represent their respective vectors as complex numbers
written in trigonometric form, and solve for the resultant
force.
60.
Resultant Force.
Force
A
, at 40 pounds, and force
B
, at
50 pounds, make an angle of
with each other. Represent
their respective vectors as complex numbers written in
trigonometric form, and solve for the resultant force.
45°
100 lb
Force
A
120 lb
Force
B
30º
30°
61.
Resultant Force.
Force
A
, at 80 pounds, and force
B
, at 150
pounds, make an angle of
with each other. Represent
their respective vectors as complex numbers written in
trigonometric form, and solve for the resultant angle.
62.
Resultant Force.
Force
A
, at 20 pounds, and force
B
, at
60 pounds, make an angle of
with each other. Represent
their respective vectors as complex numbers written in
trigonometric form, and solve for the resultant angle.
63.
Resultant Force.
Refer to Section 8.4, Exercise 85. Express
the vectors
corresponding to the dogs as complex
numbers written in trigonometric form, and find the
resultant force
to keep the system in equilibrium.
64.
Resultant Force.
Refer to Section 8.4, Exercise 86. Express
the vectors
as complex numbers written in
trigonometric form, and find the resultant force
to keep
the system in equilibrium.
65.
Resultant Force.
Refer to Section 8.4, Exercise 75. Express the
resultant vector
as a complex number in trigonometric form.
66.
Resultant Force.
Refer to Section 8.4, Exercise 76. Express the
resultant vector
as a complex number in trigonometric form.
R
S
R
S
z
S
u
S
,
v
S
,
w
S
w
S
u
S
,
v
S
60°
30°
67.
Express
in polar form.
Solution:
Find
r
.
Find
Write the complex number in polar form.
This is incorrect. What mistake was made?
z
=
1
73
(cos
69.44°
+
i
sin
69.44°)
u
=
tan

1
a
8
3
b
=
69.44°
tan
u
=
8
3
u
.
r
=
2
x
2
+
y
2
=
1
9
+
64
=
1
73
z
= 
3

8
i
68.
Express
in polar form.
Solution:
Find
r
.
Find
Write the complex number in polar form.
This is incorrect. What mistake was made?
z
=
1
73
[cos(

69.44°)
+
i
sin(

69.44°)]
u
=
tan

1
a

8
3
b
= 
69.44°
tan
u
= 
8
3
u
.
r
=
2
x
2
+
y
2
=
1
9
+
64
=
1
73
z
= 
3
+
8
i
In Exercises 67 and 68, explain the mistake that is made.
69.
In the complex plane, any point that lies along the
horizontal axis is a real number.
70.
In the complex plane, any point that lies along the vertical
axis is an imaginary number.
71.
The modulus of
z
and the modulus of
are equal.
72.
The argument of
z
and the argument of
are equal.
73.
Find the argument of
where
a
is a positive real number.
z
=
a
,
z
z
74.
Find the argument of
where
b
is a positive real number.
75.
Find the modulus of
where
b
is a negative real
number.
76.
Find the modulus of
where
a
is a negative real number.
In Exercises 77 and 78, use a calculator to express the complex
number in polar form.
77.
where
78.
where
a
7
0

3
a

4
ai
,
a
7
0
a

2
ai
,
z
=
a
,
z
=
bi
,
z
=
bi
,
■
A P P L I C AT I O N S
■
C ATC H T H E M I S TA K E
■
C O N C E P T U A L
In Exercises 69–72, determine whether each statement is true or false.
914
CHAPTER 8
Additional Topics in Trigonometry
Graphing calculators are able to convert complex numbers
from rectangular to polar form using the
abs
command to
find the modulus and the angle command to find the angle.
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 Summer '17
 juan alberto
 Complex Numbers, Sin, Cos, Complex number