Yes, I have just taken and finished Introductory Algebra a month and two days ago and am moving on to Intermediate Algebra and wondering if any person/expert could tell me about these two types of numbers.

A real number is roughly any number and a complex number is roughly a number containing an imaginary unit which is 'i'.

4 is a real number
4i is a complex number
2+4i is another complex number

Here, i is such that

i^2 = -1

I'm sure that you have seen at least once, where you had a quadratic like

y = x^2 - 4x + 8

And you tried to find the roots but you got something like:

x =2 \pm \sqrt{-4}

And stopped there saying that there were no solutions since there is the square root of a negative number.

Strictly speaking, there are solutions, but they are complex roots. You are used to find real roots, but in complex numbers, you also deal with complex roots.

This one, for example will have the complex(or imaginary) roots:

x = 2 + 2i

x = 2 - 2i

More details on the web: http://en.wikipedia.org/wiki/Complex_number

If you have more questions, don't hesitate to ask :)