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🎶

about 22 hours 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.

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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.

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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.

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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.

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July 9, 2024 at 10:52am

#1073711

Seoul Blues

Another entry for this round of "Journalistic Intentions"

[18+], in which I demonstrate that I've got no

Seoul

While I like to travel (apart from the whole "airplane" bullshit), there are some places in the world that I would actively avoid. Kabul, for example. Mount Everest. East St. Louis.

There also exist locations I definitely want to go to (which is distinct from "will definitely visit.") Places like Tokyo or Budapest, e.g.

Seoul, South Korea is smack in the middle of these extremes.

I'm sure the city has its charms. The pictures I've seen look pretty enough. There's nothing that would make me say, "yeah, not going there." I simply have other priorities.

Now, if someone were to go, "Yo, Waltz, wanna visit Seoul with me?" I'd probably say yes. Assuming I liked the person, of course. But if I only get one chance to visit that general area of the world, it'd be to sample the whiskey, sake, and delicious cuisine on the other side of the Sea of Japan.

I mean, sure, there's the whole "awfully close to their northern enemy" thing. But that wouldn't stop me. Everywhere has its risks, including sitting on one's ass at home.

Despite having been mostly destroyed during Japanese occupation (or attempted Japanese occupation; I've always been a little unclear on that particular war), the city and surrounding area apparently has lots of really cool historical tourist traps: palaces, temples, and the like. But the primary reason I travel is to experience culture, by which I mean yeast culture. And there's nothing that stands out in Korea in terms of food or drink.

Right now some of you are going, "You're nuts. Korean food is delicious." You're right; it is (or at least what makes it over here is). Except kimchi. Fuck kimchi. But so are a lot of other national cuisines.

Apparently, one of the big tourist draws of Seoul is the shopping. I'm not interested in yucking other peoples' yum, but I have near-zero interest in that activity. You know who else supposedly has great shopping? France. You know what I haven't mentioned once in my banging on about planning to visit France? Shopping.

That leaves art and architecture, and I'd definitely check some of that out if someone dragged me there.

None of this is meant to rag on Seoul in particular or South Korea in general. They're cool. I just have no more desire to visit there than I do Omaha. And at least I can drive to Omaha.

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