How do we use imaginary numbers?

               When using the quadratic formula to solve quadratic equations we sometimes run into problems. When finding the discriminant (√b²-4ac) that number can come out to be negative. Here's an example:

      How are you supposed to find the square root of -4? Impossible, right? You may be thinking "Oh. There must be no solution." But there is and using imaginary numbers you can find that solution. An imaginary number is represented by  ,and will help you find your answer.  is the answer to the √-1. This allows us to find the square root of a negative number. Hurray! Lets apply this to √-4.

     First we get rid of the √-1 from √-4 this will leave you with √4. Getting the gist? The problem becomes a breeze from here. Because you know 4 is a perfect square you just simplify and get 2. Don't forget about your imaginary component. The  goes after all real numbers, and before square roots. Making your final answer 2. Piece of cake huh? That my children, is how you use imaginary numbers when solving a quadratic equation.