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626 ⏐⏐⏐ THE BASIC ELEMENTS AND PHASORS
*37. For the network of Fig. 14.78 and the applied signal:
a. Determine i 1 and i 2.
b. Find i s.
e
+
–
i s
C 1
i 1
2 mF
e = √ — 2 100 sin (10 4 t + 60°)
+
–
v s
FIG. 14.78
Problem 37.
i s = √ — 2 6 sin (10 3 t + 30°)
i s
L 1
i 1
4 mH
FIG. 14.79
Problem 38.
C 2
L 2
i 2
i 2
8 mF
*38. For the network of Fig. 14.79 and the applied source:
a. Determine the source voltage v s.
b. Find the currents i 1 and i 2.
12 mH
SECTION 14.9 Conversion between Forms
39. Convert the following from rectangular to polar form:
a. 4 � j 3 b. 2 � j 2
c. 3.5 � j16 d. 100 � j 800
e. 1000 � j 400 f. 0.001 � j 0.0065
g. 7.6 � j 9 h. �8 � j 4
i. �15 � j 60 j. �78 � j 65
k. �2400 � j 3600
l. 5 � 10 �3 � j 25 � 10 �3
40. Convert the following from polar to rectangular form:
a. 6 �30° b. 40 �80°
c. 7400 �70° d. 4 � 10 �4 �8°
e. 0.04 �80° f. 0.0093 �23°
g. 65 �150° h. 1.2 �135°
i. 500 �200° j. 6320 ��35°
k. 7.52 ��125° l. 0.008 �310°
41. Convert the following from rectangular to polar form:
a. 1 � j 15 b. 60 � j 5
c. 0.01 � j 0.3 d. 100 � j 2000
e. �5.6 � j 86 f. �2.7 � j 38.6
42. Convert the following from polar to rectangular form:
a. 13 �5° b. 160 �87°
c. 7 � 10 �6 �2° d. 8.7 �177°
e. 76 ��4° f. 396 ��265°
SECTION 14.10 Mathematical Operations with
Complex Numbers
Perform the following operations.
43. Addition and subtraction (express your answers in rectangular
form):
a. (4.2 � j 6.8) � (7.6 � j 0.2)
b. (142 � j 7) � (9.8 � j 42) � (0.1 � j 0.9)
c. (4 � 10 �6 � j 76) � (7.2 � 10 �7 � j 5)
d. (9.8 � j 6.2) � (4.6 � j 4.6)
e. (167 � j 243) � (�42.3 � j 68)
f. (�36.0 � j 78) � (�4 � j 6) � (10.8 � j 72)
g. 6 �20° � 8 �80°
h. 42 �45° � 62 �60° � 70 �120°
44. Multiplication [express your answers in rectangular form
for parts (a) through (d), and in polar form for parts (e)
through (h)]:
a. (2 � j 3)(6 � j 8)
b. (7.8 � j 1)(4 � j 2)(7 � j 6)
c. (0.002 � j 0.006)(�2 � j 2)
d. (400 � j 200)(�0.01 � j 0.5)(�1 � j 3)
e. (2 �60°)(4 �22°)
f. (6.9 �8°)(7.2 ��72°)
g. 0.002 �120°)(0.5 �200°)(40 ��60°)
h. (540 ��20°)(�5 �180°)(6.2 �0°)
45. Division (express your answers in polar form):
a. (42 �10°)/(7 �60°)
b. (0.006 �120°)/(30 ��20°)
c. (4360 ��20°)/(40 �210°)
d. (650 ��80°)/(8.5 �360°)
e. (8 � j 8)/(2 � j 2)
f. (8 � j 42)/(�6 � j 60)
g. (0.05 � j 0.25)/(8 � j 60)
h. (�4.5 � j 6)/(0.1 � j 0.4)
*46. Perform the following operations (express your answers
in rectangular form):
(4 � j 3) � (6 � j 8)
a. ���
(3 � j 3) � (2 � j 3)
b.
c.
d.
8 �60°
���
(2 �0°) � (100 � j 100)
(6 �20°)(120 ��40°)(3 � j 4)
����
2 ��30°
(0.4 �60°) 2 (300 �40°)
���
3 � j 9
3
1 2 1
e. �� � 2 �� �� �� 2
(0.02 �10°) 6 � j �9�0�0� �
� j
�