You may want to review simplifying roots first.
As you know, you can't take the square root of a negative number. But mathematicians (and, by “mathematicians”, I mainly mean Gerolamo Cardano, a professional gambler who lived in what's now Italy in the 1500s) have noticed that it's often useful to essentially pretend you can. That is, we make up a number called i with the property that i2 = −1. Now, of course, √−1 = i.
If this bothers you, bear in mind that this is really no different from √2. In the old days, the only numbers that were thought of as “real” were rational numbers. But it was useful to invent a number whose square was 2, so people did. Similarly, it's useful (in a number of fields) to invent a number whose square is −1, so we do that. Of course, unlike √2, i doesn't appear anywhere on the number line. When we want to refer specifically to numbers on the number line, we'll call them real numbers.
Now, we can take the square root of any negative number. For example, √−12 = √−1 * √12 = i * 2√3 = 2√3*i.