Types of Numbers - Imaginary Numbers

Last week I told you about the building blocks of numbers, the number line. I also said that these numbers are not sufficient to solve every equation possible. Imagine you had the equation:

x^2 = -1

(You probably know x^2 means x squared, but I just thought I'd check!)

At this point you are probably thinking, "but you can't have a negative square number," which is absolutely right, if you are dealing with real numbers. So the answer to the question of how to solve the equation is to not look at real numbers. This is where imaginary numbers come in.

An imaginary number is represented by the letter i. i is equal to the square root of -1, so as you can probably guess, the answer to the above equation is in fact:

x = i

This is a very strange concept for some people, because imaginary numbers are not something that you can imagine in real life. Whole numbers, fractions and even irrational numbers are easily translated into real life problems, but imaginary numbers are an abstract concept.

There is another type of number that uses imaginary numbers. These are called complex numbers. These are simply numbers of the form a + bi, where a and b are real numbers. All previous numbers I have talked about are complex numbers too. If we take a or b to be equal to zero (in maths, or usually means one or both) then we can see how real numbers and imaginary numbers are both of the same form as complex numbers.

Complex numbers can create some very beautiful things. For example, take the Mandelbrot Set.

Mandelbrot Set

Zoomed in

This is an example of a fractal, which is created by feeding the result of z^2 + c (where z and c are both complex numbers) back into z.

Monday Maths Madness 22

I was debating whether to call this number 22 or 23, but I decided Christmas Maths Madness was a different thing, so I'll resume from where I left off. Because you really wanted to know that.

This is one of those internet memes. Normally it says "*something* is too damn high". I like two damn pi though. I wish I had two damn pies. That would make me very happy right now. *end random tangent*

Complex numbers (erm, relationships?) gotta love them.

I love it when people answer silly questions completely literally. This guy clearly put a lot of thought into his answer, and it kind of makes sense!

Well that's it from me today. I might actually write something worth reading on the next Monday Maths Madness. You never know. You'll have to stick around to find out... :P