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.