Johnny, a 15 year old male from Mississauga asks on October 10, 2003,

In math class, my teacher has been frequently making references to what I've mentally labelled, as "imaginary numbers". Interestingly, he's explained to us that in our level of mathematics, while completing the square and finding roots of certain trinomials, one can end up with the square root of a negative number. He explained that in this case, we can substitute this "number" with the variable, "i". He referred to it as part of a group of numbers called 2-D numbers and he has also been making references to Complex Number Fields and other such number fields. My question is: what exactly are 2-d Numbers? What is the Complex Number Fields? And what are examples of such other "fields"?