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Solutions:
a. By Eq. (14.34),
b. Using an alternative method, we obtain
�4 � j 8
�6 � j 1
�24 � j 48
� j 4 � j 2 8
�24 � j 52 � 8 ��16 � j 52
�6 � j 1
�6 � j 1
36 � j 6
� j 6 � j 2 1
36 �0 � 1 � 37
�16 j52
and � ������0.432 �j1.405
C2 37 37
To divide a complex number in rectangular form by a real number,
both the real part and the imaginary part must be divided by the real
number. For example,
� 4 � j 5
6.8 � j 0
and �� � 3.4 �j 0 � 3.4 �0°
2
In polar form, division is accomplished by simply dividing the magnitude
of the numerator by the magnitude of the denominator and subtracting
the angle of the denominator from that of the numerator. That
is, for
C1 � Z1 �v1 and C2 � Z2 �v2 we write
C1 (1)(4) � (4)(5) (4)(4) � (1)(5)
� ��� �j��
2 2
2 2
C2 4 � 5 4 � 5
24 j 11
�����0.585 � j 0.268
41 41
C 1
8 � j 10
� 2
C 1
� C2
� / v Z1 � 1 � v2 (14.35)
Z2 EXAMPLE 14.25
a. Find C1/C2 if C1 � 15 �10° and C2 � 2 �7°.
b. Find C1/C2 if C1 � 8 �120° and C2 � 16 ��50°.
Solutions:
C1 15 �10° 15
a. � ��� � /10° � 7° � 7.5 �3°
C2 2 �7° 2
MATHEMATICAL OPERATIONS WITH COMPLEX NUMBERS ⏐⏐⏐ 605