356 Imaginary and Complex Numbers
− 5 −j 3
1 −j 6
0 + j0
When a complex number is written as a difference between a real number and an imaginary
number, we can rewrite it as a sum. The third and fourth of the above complex numbers can
be converted to the sums
− 5 + (−j3)
and
1 + (−j6)
The complex numbers 0 +j0 and 0 −j0 are the same as the real number 0. They are also
identical to the imaginary numbers j0 and −j0.
The complex-number plane
The set of complex numbers needs two dimensions—a plane—to be graphically defined.
The set of coordinates shown in Fig. 21-4 is the complex-number plane, in which we can plot
(^6) - 4 - 2 246
j 6
j 4
j 2
j 2
- j 4
j 6
(-4,+j5)
(4,+j3)
(-5,-j3)
(1,-j6 )
a
jb
Origin = 0 + j 0
= 0
Figure 21-4 The complex-number plane, showing
five values plotted as points. The
dashed reference lines help to show the
coordinates of the points on the axes.