Basic Math and Pre-Algebra For Dummies (107 page)

 If
isn't on the real number line, where is it? That's a good question. For thousands of years, mathematicians believed that the square root of a negative number was simply meaningless. They banished it to the mathematical nonplace called
undefined,
which is the same place they kept fractions with a denominator of 0. In the 19th century, however, mathematicians began to find these numbers useful and found a way to incorporate them into the rest of math.

Mathematicians designated
with the symbol
i.
Because it didn't fit onto the real number line,
i
got its own number line, which looks a lot like the real number line. Figure 
25-1
shows some numbers that form the imaginary number line.

Even though these numbers are called imaginary, mathematicians today consider them no less real than the real numbers. And the scientific application of imaginary numbers to electronics and physics has verified that these numbers are more than just figments of someone's imagination.

A
complex number
is any real number (see “Getting Grounded in Real Numbers,” earlier in this chapter) plus or minus an imaginary number (see the preceding section). Consider some examples:

• 1 +
  i
   5 – 2
  i
   –100 + 10
  i