Complex Numbers (Book)

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Complex Numbers

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

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Write_Mikey_Write!

about 5 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

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Adherennium Plotting something

about 7 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

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Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

December 11, 2023 at 1:04am

#1060864

Revisited: "Cosmological Comedy"

I usually take another look at old entries on Sundays, but because I found that Betelgeuse eclipse thing and wanted to share it, I'm digging into the archives today (Monday), instead.

As an aside, I've now been doing these Revisited entries for over a year, which means that some of the older ones would be eligible for a second revisit... except I've decided to exclude those, too.

This one's not very old, from the end of September of last year: "Cosmological Comedy"

, featuring a Cracked article

on some purportedly mind-blowing ideas about the universe, or at least parts of it.

Me: You can go down your own YouTube rabbit hole...

YouTube has been going downhill in general, but since I wrote that entry, the enshittification increased exponentially. I despise ads; it despises ad blockers. So I don't go to YouTube nearly as often, these days.

Article: 5. Do We Have Another Planet?

I've done a couple of more recent entries, earlier this year, about what I've taken to calling Planet Ix, as a play on the older hypothetical Planet X and the roman numeral for nine. While doing so, I seem to have forgotten about this entry from last September that also talked about it.

The 2022 article also speculated: A much more excellent idea is that P9 isn’t a planet but a black hole. A primordial black hole, dating to the first second of creation. As in, the first second ever.

Which I mocked, but to be clear: it would be amazingly cool if this were the case, because we'd actually have the capability, theoretically, to send a probe to study a black hole up close (relatively speaking). It would take a long time, sure, but not nearly as long as trying to visit another solar system.

Apart from that section, I couldn't find anything else worthy of updating or correction. After all, it hasn't been all that long. The topics also may very well come up in future entries again.

Not this week, though. I'm going to start heading home today, most likely a five-day journey (depending on weather and whatever other stuff the universe can throw at me), during which I won't be arsed to make longer blog entries... unless something happens that I need to rant about.

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