Complex Numbers
The main thing to understand is that Complex Numbers are a way to express numbers on a 2D plane, which is a useful abstraction for concepts such as those in Fourier Transforms
You cannot generally take the square root of -1, so a shorthand way of writing the sqrt(-1) would be to write it as i. This, or any constant multiplication of it (IE, 3i) is known as an imaginary number,
You are likely familiar with the Number Line, a line where numbers are ordered and goes across one direction. Imagine that line to be the X axis, and the Y axis are imaginary numbers.
In this coordinate system, we write a point as the real number + the imaginary number multiplied by i. So in the above answer we would write that point as 3 - 4i.
You can also think of these as vectors of x and y components. That means we can also find the magnitude of these vectors via the Pythagorean theorem (the magnitude of the above vector would be "5" for example).
The reason this is useful is in the above example. Without imaginary numbers, a point at 3 + 4i and 3 - 4i would appear the same because the real number "3" is identical in both, however one can see on the complex plane they would actually represent different points entirely.
This additional context becomes important for understanding Fourier Transformations.
Before continuing, be sure to understand the previous 3 pages pretty well as we will now combine ideas!