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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Brandiwyn🎶

a day ago
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.

1 Like

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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

November 20, 2021 at 12:01am

#1021994

People Eating Tasty Animals

Don't we have enough crazy conspiracy "theories" in the world already?

PROMPT November 20^th

In your blog tonight/today, write about a story you've been told, or use a newscast story and CREATE a conspiracy theory. Tell us why you chose this subject, and of course, provide 'evidence' that your theory could be rooted in truth.

Earth is flat, the moon landing never happened, JFK was assassinated so Johnson could take office, 9/11 was an inside job, the Holocaust never happened, aliens built the pyramids, and Santa Claus isn't real.

While planning for the 2017 solar eclipse trip, I noticed that the path of totality crossed Yellowstone, so I got an idea. Other people start crazy just-barely-plausible rumors that get repeated as fact (such as the one where you can only balance an egg on its small end on the equinoxes -- sorry if you bought that one, but it's utter tripe), why not start one of my own?

So I started putting out there that during the eclipse, the combined gravity of the sun and moon would be just enough to trigger the Yellowstone Supervolcano. I felt dirty doing it, though. It's complete nonsense couched in semi-plausible astronomical language. True, an eclipse can only happen during a conjunction, and during conjunctions (eclipse or not) ocean tides are measurably higher. But there's no way it could be strong enough to trigger a supervolcano, at least not particularly during an eclipse. The gravitational effect isn't significantly different than during any new moon (or full moon for that matter).

Unfortunately (actually, fortunately), I don't have nearly enough influence online for that to catch on, and it didn't "go viral."

But... that's not really a conspiracy theory; that's just more spreading bullshit, and I've since sworn off that particular method of trolling.

So. This is one I've been knocking around in my head for a while:

Consider PETA.

Buncha loonies, trying to move the center by being so extreme that "middle ground" gives more rights to animals. But what if, at the top, they're not actually animal rights activists, but instead have a more honest motive?

Like money.

See, everything about PETA starts to make perfect sense if you accept that it's being directed by business interests -- specifically, companies such as soybean growers and fake fur manufacturers. If they can push veganism more into the mainstream, we'll need more soybeans, right? For tofu and other disgusting concoctions. And the fake fur thing is obvious; I mean, hardly anyone wears fur anymore anyway, but they still need to grow their business, right?

I'm sure you can think of other business interests that would be aided by such a shift.

Why do I choose this subject? Well, I like animals -- some of them are delicious. And PETA is, shamefully, based here in Virginia. Also it was simply the first thing that came to mind after my failed attempt at eclipse fearmongering.

As for more evidence, well, consider that PETA operates an animal shelter with an abnormally high kill rate.

Does that sound like an organization that truly believes animals have the same rights as humans? So there must be another agenda at work. We don't eat dogs or cats (usually), so they're not competing with the tofu industry; therefore, it doesn't matter to the organization if they're alive or not.

Still, I have to admit I miss their naked protests. Those always made me hungry, and I'd have to go out and get a big thick juicy steak whenever I saw one.

Anyway, I should note that I have not one single shred of evidence that business interests are behind their craziness. But it wouldn't surprise me in the least if I turned out to be right.

7 Like • Comment • View 5 comments

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