Algebra Know-It-ALL

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.