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any number not on the real axis would not exist—hence the term imaginary
for the vertical axis.
In the complex plane, the horizontal or real axis represents all positive
numbers to the right of the imaginary axis and all negative numbers
to the left of the imaginary axis. All positive imaginary numbers are
represented above the real axis, and all negative imaginary numbers,
below the real axis. The symbol j (or sometimes i) is used to denote the
imaginary component.
Two forms are used to represent a complex number: rectangular
and polar. Each can represent a point in the plane or a radius vector
drawn from the origin to that point.
14.7 RECTANGULAR FORM
The format for the rectangular form is
–
0
j
–1
–2
–3
–4
–5
–6
–j
–6
C = 0 – j6
+
(14.20)
as shown in Fig. 14.36. The letter C was chosen from the word “complex.”
The boldface notation is for any number with magnitude and
direction. The italic is for magnitude only.
EXAMPLE 14.13 Sketch the following complex numbers in the complex
plane:
a. C � 3 � j 4
b. C � 0 � j 6
c. C ��10 � j20
Solutions:
a. See Fig. 14.37.
b. See Fig. 14.38.
c. See Fig. 14.39.
14.8 POLAR FORM
The format for the polar form is
C � X � jY
FIG. 14.38
Example 14.13(b).
C � Z �v
with the letter Z chosen from the sequence X, Y, Z.
(14.21)
– 0 1 2 3
–
–10
C = –10 – j20
j
1 2
4
3
j
–10
–j
+3
j
0
–20
–j
–20
C = X + jY
– +
X
–j
POLAR FORM ⏐⏐⏐ 597
FIG. 14.36
Defining the rectangular form.
+4
FIG. 14.37
Example 14.13(a).
FIG. 14.39
Example 14.13(c).
C = 3 + j4
+
Y
+