Many times when solving problems in algebra we obtain answers like –2,
,
,
and so on. All of these are considered
real numbers.
However, not all problems can be solved with a real number answer. There are some occasions when we have to work with a different type of number called a
complex number. A
complex number takes on the form
where
is called the real part and
is called the imaginary part. Since we’ve already listed some examples of real numbers, let’s take a look at the imaginary part.
When we have a situation like
we have to begin dealing with
imaginary numbers. We define an
imaginary number 
to be
.
So whenever a negative number appears in a
square root, we can take the
square root of that negative and call it
. Then we are left with just
.
So our answer is
.
This is where the imaginary part of a
complex number comes from.