move down by −5 units, which means we really move up by 5 units. We finish at the point corresponding
toj2. We can write
−j 3 − (−j5)=j 2
Simplifying, we can write
−j 3 +j 5 =j 2
Real + Imaginary = Complex
When you add a real number and an imaginary number, you get a complex number. In this
context, the term “complex” does not mean “complicated.” A better word would be “compos-
ite,” but that term has already been taken! (A composite number is a natural number that can
be factored into a product of two or more primes.) All the rules of arithmetic you learned in
Chap. 9 apply to complex numbers, complex-number variables, and expressions containing
complex numbers.
How they are written
When we write a complex number, we put down the real-number part first, then a plus or
minus sign, and the imaginary-number part. Here are some examples:
4 +j 3
− 4 +j 5
Start here
Finish here
Move downward
by-5 units
j 3
j 2
j
0
Figure 21-3 Here, we start
with−j3 and then
subtract−j5, ending
up with j2. When
we go negatively
downward, we
go upward by the
equivalent distance.
Real + Imaginary = Complex 355
