Complex Numbers, Part 7 - Why We Need Them, Continued

Complex numbers. An explanation of why they are necessary.

Category:

Education

Tags:

• complex
• imaginary
• complex numbers
• imaginary numbers
• homeschool
• math
• homeschool math
• Derek Owens

[MrAlexGTV]

If the universe is digital as quantum theory seems to suggest (energy quanta, Planck length, Plank time etc.) the real "real" numbers are only integers.

[derekowens]

@MrAlexGTV Or rather, integer multiples of the Planck constant.

[3bood1st]

Do u have a video about changing from complex to polar ??

[derekowens]

@3bood1st In my Precalculus class, I do cover some topics on complex numbers in polar form. The videos are very old and low quality, though. I need to re-record them before I post them for the public to see.

[frankr29]

A revealing statement is made at 6:00 of this video: "... irrational numbers show up in the real world, so we need to add those to our system of numbers." The same is true for the rational numbers, etc. that came before, but it is NOT true for the imaginary/complex numbers that come after. The ONLY rationale for these numbers is algebraic closure. This is why, in my view, using the word "numbers" for so-called imaginary numbers is fundamentally misleading. Any comments, Derek?

[derekowens]

Thanks!

There actually are some answers to that question. I can name two:

1) I really like this stuff. In other words, I'm pretty internally motivated.

2) I'm externally motivated also. Most teachers teach in a school, in which their pay is set by the bureaucracy. Even if they do a great job, they get the same pay. I work in the free market. My compensation depends on the job I do for my clients. So I'm motivated to improve, to innovate, and to do the best I can.

[realrockstar786]

this has broaden my concept of maths n its importance.nw i certainly will love doing maths. thanks lot

[derekowens]

@7PunkCyber Yes, thanks. Tell me, though, in the AC circuit analysis, doesn't the imaginary part typically get dropped at the end, leaving only the real part as the actual meaningful value?

[derekowens]

@mbarkhau Okay, I'll grant you that. Existence can refer to material objects, not concepts. One might argue the point, though. Also, my understanding of complex numbers has changed since I recorded these videos, and doing a little editing is on my ToDo list. They don't seem to be actual numbers in the same sense that real numbers are. If real numbers are called "real" because they can be used to represent real things, then imaginary numbers are called imaginary because they cannot.

[mbarkhau]

@derekowens While we are nit picking. I have a problem with using the word "exists" in the context of numbers. Numbers don't exist, they are concepts which can be meaningful or meaningless. A tree exists, an apple exists, you and I exist. Numbers don't exist, neither do laws or rights or society. But just because they don't exist, doesn't mean the concepts aren't useful to make sense of the world.

[nigellimjr]

helped alot. sweet

[oHeyitsthatguy]

hah, make a box pi units by pi units exactly - infinite space ._.

Problem? :)

Very good video thanks.