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 13

Back to pictures this week. My boyfriend keeps sending me links to pictures on 9gag.com that are maths related, so I have enough to do a post about them!

This is a bit what I feel like in my lectures at the moment! Especially Analysis. You think it's simple, but when you actually come to write it down, there are no words to explain it.

The square root of a negative number is called an imaginary number. Anything else is a real number. Squaring an imaginary number makes it real. Shit just got real.

This is my personal favourite. I'm doing a lot about planes in Intro to Geometry at the moment. So far there have been no snakes though... Just triangles.