Complex Numbers

[Curbie]

My life is settling down again after building two new machines for me, evaluating and loading a new OS distro, and evaluating loading some new applications to carry-on with meeting my needs. Now I’m back going though python tutorials looking for and trying to answer questions unintentionally brought up by the tutorial.

This is the third or forth pass I’m going through all about 40 basic python tutorials, and about 40 GUI tutorials, both groups of code made and published by w3schools. For me is better to push through the initial unintended questions on the first few passes, because a lot of times they’re answered later in the tutorial or in later tutorials, or may just “click to me” later.

If there are still questions at this point, I don’t think more passes will answer it, so to the web, then here.

Complex numbers for me, bring up the unintended question of, the tutorial explains they exist and how to store them, but not what their used for. Complex numbers seem to be a higher level math concept, that if you don’t know how it's used, you probably don’t have need of them, although I did see some geometry examples, which may mean it may have use in geometry, GPS coordinates, or graphic?

Am I on the right track, or still missing the programming purpose and uses of complex numbers?

curbie

[Gribouillis]

Complex numbers are heavily used by mathematicians. They are used in almost all fields of mathematics, geometry, analysis, algebra, number theory etc.

Complex numbers are also used by physicists. They are particularly useful when there are harmonic waves propagation, for example in elecromagnetism and fields theory. Some famous equations such as the Schrödinger equation cannot even be written without complex numbers. These numbers cannot be avoided in the study of the spectral properties of operators that appear everywhere in physics. Even the spectral properties of simple matrices use complex numbers and these properties have a crucial impact on the phenomenons that these matrices represent.

I know that some applications in robotics use complex numbers and generalizations such as quaternions and Clifford algebras. I guess digital image processing uses complex numbers, so do all domains that use the famous FFT or fast Fourier transform algorithm, such as signal processing.

Let me conclude by saying that complex numbers are not that complex, there are only a few concepts to grasp and a few rules to learn how to calculate with them. You'll easily find a simple online course about complex numbers.

[Curbie]

Thanks Gribouillis,

"Complex numbers" is a higher level math concept, next time I need geometry, analysis, algebra, number theory and harmonic wave propagation, I'll know where to turn, but for now, I know what they are and where they're typically used, it seems to me they are not particularly useful in newbee tutorials and could be skipped until needed. I learn way better, when I'm learning new concept building towards a goal.

But now I seem to have an answer to that unanswered question (a sliver in my brain) I should be able to let it go, looking for the next unanswered question, it's getting better, but still have a ways to go.

curbie

[Gribouillis]

it seems to me they are not particularly useful in newbee tutorials and could be skipped until needed.

In beginner's OOP courses, complex numbers can be used as an example of implementing a class with definitions of arithmetic operators + * - / as well as the absolute value etc. That could be the context where you met them in the tutorials.

[bowlofred]

I often use complex numbers when I am implementing a 2D grid. I can implement motion by just adding numbers in the correct direction. Rotations are just multiplications.

It's not magic, but it does make some operations simpler (perhaps at the cost of converting the XY coordinates into and out of complex numbers).