i

There is a number in maths that may or may not exist depending on which set of numbers you are looking at...

i - or, more precisely, √-1.

It's the solution to the polynomial x^2 + 1=0. If you only used the real numbers, then there would be no way to find an x that solves this equation. Only if you also allow complex numbers to be used to solve this equation will you get a solution: i and -i.

Obviously, since i = √-1, i^2 = -1. Which is nice and all, but where can you find i?

It is important to state that i is also the component of a complex number. i is equal to 0+1i, which you'll note is of the form a + bi, where a and b are real numbers. You can plot this on a complex plane, with complex values along the y-axis and real values along the x-axis (in an Argand diagram - much like the Cartesian plane in a way).

One place is the Schrodinger equation, which is very important in the field of quantum mechanics (source of image - Wikipedia). I will not try to explain the equation - I am hardly the kind of person who could - and I apologise for that. But there's i, at the beginning - how lovely! (I have to mention, however, that this equation here is time-dependent - so when time causes the potential energy of the system to change - there is a different, time-independent equation which doesn't involve i). More here

There's also the Mandelbrot set, which involves a function: f(x) = x^2 + c, (c being a complex number here) and plotting the resultant complex values that do not diverge onto a complex plane. You start at x=0, and plug in a certain complex value, which, after multiple iterations (the value that comes out of the function becoming your new x), if the resultant function diverges, that complex value is not in the Mandelbrot set. Once the values have been plotted, you get a fractal that forms - the values in black on the below image (source - Wikipedia) are in the Mandelbrot set.

 

I am frankly not qualified to write about i, but I hope this has been a good enough blogpost about some uses of i. It is also hopefully not incorrect, and if it is, I will strive to correct this post over time... 

Yes, I realise that one of the labels for this blogpost is "article" - hopefully this passes as such...