Algebra Know-It-ALL

360 Imaginary and Complex Numbers

The line segment connecting (3, j ) and (5, j 4) is opposite from the side with slope m 1. Let’s call its slope

m 2. Then

m 2 =Δjb/Δa

= ( j 4 −j)/(5− 3)

=j3/2

These two opposite sides are parallel. We’re halfway there! Now let’s find the slope m 3 of the line segment

connecting (2, j3) and (5, j4). It is

m 3 =Δjb/Δa

= ( j 4 −j3)/(5− 2)

=j/3

Finally, let’s find the slope m 4 of the line segment connecting (0, j 0) and (3, j ). This line segment is oppo-

site from the side with slope m 3. We have

m 4 =Δjb/Δa

= ( j− 0)/(3 − 0)

=j/3

2 4 6

j 6

j 4

j 2

a

jb

(0,j0)

(2,j3)

(5,j4)

(3,j)

Slope = m 1

Slope = m 2

Slope = m 3

Slope = m 4

Figure 21-5 Addition of (2 +j3) and (3 +j), illustrated in the

complex-number plane.