Can you explain what imaginary numbers are and how they fit in the larger scheme of number systems in terms...

first of all, you need to know that there are basically two types of numbers. Real and imaginary.

real numbers are those which can be represented in one form or another, but they exist in real world. for example, if you say that there are 4 trees, that means that you can count the number of trees to be a distinct value, ie., 4.

or consider this. the probability of an event happening is 0.58. this means that the event will be successful 58 times if it is performed 100 times.

real numbers consist of all the rational, irrational numbers. that means all these can be realised to be present.

now coming to imaginary numbers, these are not actually present.

consider a number like sqrt(-1). we all know that a square root of a negative number doesnt exist. so, we just say that sqrt(-1) doesnt exist. such numbers can be conveniently represented as Imaginary Numbers. these numbers donot mean anything in the real world, but help in our mathematical calculations.

now, hope this answers your question....

What is an imaginary number? What is i?

Contrary to what some people might tell you, imaginary numbers are not numbers that only exist in the brains of weird people. Or maybe they are; all numbers in math are "imaginary" in the sense that you can't touch them or experience them directly.

But this is not what people mean when they talk about imaginary numbers. Imaginary numbers are numbers that can be written as a real number times i.

So what is a real number, and what is i?

Well, the real numbers are all the positive numbers, negative numbers, and zero. These are numbers like

5

-2.9

-4/3

0

1.11211211111221312211131122211113213211...

(bonus points if you can tell us

what the next few digits are and why!)

So the real numbers are the numbers that you probably already know: they're the ones on the number line.

What is i? It's the square root of -1 (see footnote below). And it's NOT a real number. i was invented because people wanted to be able to take square roots of negative numbers, and you can't do that if you limit yourself to real numbers.

So we can make an imaginary number by taking a real number like 5 and multiplying it by i. That gives us 5i. Some other imaginary numbers are

37.3i

1.11211211111221312211131122211113213211i

Pi*i.

Note that the square of any imaginary number (except 0) is a negative number.

Complex numbers are numbers like 7 + .4i; they're a real number plus an imaginary number

Imaginary numbers is a concept to help us give a value for the square root of a negative number. Technically the square root of a negative number does not exist hence they are called imaginary numbers.

i represents an imaginary number

i squared = -1

so for example you want a value for the square root of -16

we know that 4*4=16

Given i squared = -1 , the square root of -16 is then 4i

Hope this helps =)