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
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