>> In times past when we have encountered a number like this, the square root of a negative value, we have said that this is not a real number and we have simply moved on to another problem. Well with a simple definition here, we can actually create another set of numbers, a set of numbers that is beyond the real numbers that we have been dealing with. All we need to do is find an imaginary unit I that is the square root of negative 1 and look at what happens to this problem. Now we have a representation for this problem. We can represent in a rather special way. The square root of negative 25 can be thought of as the square root of 25 times negative 1. The square root of 25 though is 5 and the square root of negative 1 by our definition here is simply I, so we have a way of representing this. Now this is an imaginary number. Now imaginary numbers fit into our overall number system like this. Now you recall that the real numbers are composed of rational numbers and irrational numbers, remember rational numbers are the numbers that can be written in the form of a fraction. Irrational numbers are the square roots of non-squares basically, never-ending, never repeating decimals. Now these two sets make up the real numbers, well now we have these imaginary numbers that we have just defined and when we put the imaginary numbers with real numbers that we are already familiar with, we have an enormous set of numbers called complex numbers. Complex numbers are defined as all of the numbers that can be written in the form A plus BI where A and B are real numbers and I is the square root of negative 1. Now this BI is an imaginary number and the A number is a real number, so complex numbers have a real part and an imaginary part and that is the reason they are called complex.