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.

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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.

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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 11, 2022 at 12:01am

#1040530

Tales from the Cryptid II: Ringdocus

Just like UFOs are only UFOs until they're identified (then they're just FOs), it's only a cryptid until you know what it is.

Beware Montana’s Shunka Warak’in, the ‘Rocky Mountain Hyena’
Is one of these crafty cryptids on display in a small museum?

Not to be confused with the Rocky Mountain Oyster.

Something has been preying on domesticated animals across the plains of Montana for centuries.

Yeah, wolves.

It has been given many names over the years, below most of which burn angry red squiggly lines when typed into Microsoft Word: Shunka warak’in. Ringdocus. Guyasticutus.

All of which would be awesome band names. Still. Wolf doesn't freak out my spell checker.

But it’s also been called the Beast and the Rocky Mountain hyena—in fact, any name but wolf, although the creature could easily be called a wolf.

Which is what I've been saying.

Perhaps that’s because wolves were extinct in the state for about half of the 20th century.

Yeah, sure they were.

Here in Virginia, and down into North Carolina, in the Blue Ridge Mountains, people occasionally claim to see a mountain lion (which also has multiple names: puma, cougar, whatever). Officially, mountain lions are extinct in the eastern part of the US. Unofficially, everyone knows there are mountain lions up there. Lamest cryptid ever: unlike the Jersey Devil or the Mothman, we're pretty sure what a mountain lion is.

I'm not saying cougars aren't cool. Just that we lack imagination when it comes to cryptids here in the Blue Ridge.

If only we had a carcass, we could figure out what this creature is once and for all.

Oh, wait. Turns out, we do. It’s on display in a museum in Montana.

There are museums in Montana?

(I know at least two of my occasional readers are from Montana. Relax. I'm joking.)

The article (which is actually a book excerpt, but whatever) goes on to describe how someone actually killed one, and it ended up stuffed and mounted because that's what we do, apparently. Then:

The ringdocus outlasted Sherwood and was on display at least into the 1980s. And then it disappeared.

Probably stolen by Bigfoot.

Or maybe a wolf.

Meanwhile, Lance Foster, a historic site preservationist, paranormal enthusiast, and member of the Ioway tribe, speculated that the beast could be a shunka warak’in, a canid non-wolf beast from Native American lore that would sneak into camps at night and make off with dogs (the name translates to “carries off dogs”).

Okay, fine. Not a wolf. Maybe Bigfoot's dog.

Apparently, they tracked down the taxidermied whatever-it-was (turns out it wasn't stolen by Bigfoot, but just transferred to a museum in the one state less likely to have a museum than Montana) and put the thing back on display.

Today, the creature is the museum’s most popular exhibit. They just call it the Beast.

And we're back to no imagination.

Or is it just a bad taxidermy mount? Only a DNA test could tell, and all interested parties have decided not to do that. The mystery of the shunka warak’in has gone on so long that nobody wants to risk solving it.

It may be the case that some mysteries are best left unsolved, but in this case, come ON. It's like when they tested hair that supposedly got rubbed off of a Bigfoot, and it turned out to be bear or cow or whatever. People still believe in Bigfoot after all that, because it's hard to prove a negative. (See my entry from last year, "Tales from the Cryptid"

.) Even though we have hard evidence that all the blurry pictures of that particular cryptid were definitely hoaxes.

It would be like refusing to test the DNA from the multiple taxidermied jackalopes

in neighboring Wyoming: they just don't want people to think that jackalopes are completely made up.

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