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.

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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.

2 Like

February 18, 2023 at 11:38am

#1045037

What the Bike?

Entry #5 into "Journalistic Intentions"

[18+] this month: Happy Ride

You know what always struck me as idiotic? And I do mean "always," as in "from the moment I first found out about it as a kid."

Gendered bikes.

It took me a while to figure out the reason for it, and to this day I'm not sure if I came up with the right idea or not: girls' bikes have the lowered crossbar to accommodate a skirt. I mean, that was the only thing I could figure out, as all genders have legs (barring accidents, disease, or thalidomide), and you don't ride a bike with your genitals, so what else could possibly be the difference?

I keep calling it a crossbar. It probably has a more proper name. But you know what I'm talking about: that upper rod between the saddle thingy and the handlebar whatchamacallit.

I may not be an expert on bicycles, okay? The ones in the linked prompt picture both have the lowered crossbar doohickey.

Anyway, it didn't help my bewilderment that where I spent my childhood, I didn't see a lot of girls wearing skirts or dresses. It was a rural area, and everyone wore pants or shorts, including my mom.

But enforcement of strict gender divides was even more of a thing back then (though I thought it was silly), so you'd see these girls riding around with their girly bikes (rarely pink) with the lowered crossbar. "They're just doing it because their parents thought: 'have girl. girl want bike. girl need girl bike. girl on boy bike may grow up to like girls.'" Or something like that; I don't know.

Worse, the "boy" bikes were considered standard, and the "girl" bikes, the aberration.

Seriously. No one rides a bike wearing a skirt, dress, or kilt, do they? I don't think I've ever seen it. Nor have I seen a woman riding a horse side-saddle except in, like, picture books or period (not that kind of period) movies. ("What has two legs on one side and four on the other?" was an actual riddle I saw in a kids' book at one point. "A horse with a lady riding." "What?")

And then I reached puberty. Most kids "hit" puberty; for me, it was more of a gradual thing. And that's when I realized the terrible, awful, what-the-fuck truth about life: in a sane world, in a world that makes sense, it should be the other way around, with the bikes for guys having the lowered crossbar. And yes, I learned that the hard way. That is a pain I will never, ever forget. I'll be lying on my deathbed, racked with cancer, diabetes, Alzheimer's, and a toothache, and I'll be like "Remember that time you racked your brand-new balls on a bike when you were 12?"

Didn't stop me from riding a bike (well... for more than a day or so, anyway). But I never did make sense out of gendered bikes.

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