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

June 2, 2024 at 10:06am

#1072011

Revisited: "Nonbinary"

As regulars know, I do these retrospectives, in part, to see what's changed about the world and in me since the original post. Usually, I don't find my attitude much different. That's not really the case with this entry from February of 2020: "Nonbinary"

Today's thing is a bit different from usual: a gender-issues retrospective from a male homo sapiens.

For starters, I cringe at "different from."

The article

in question, from 2018, is still up at this time, but I didn't re-read most of it.

Not only is the weight issue a pressing thing for many men, but I avoid online dating specifically because most of the women on there specify 6' or taller.

That's actually not the only reason I avoid online dating. But I wonder what some of these women's reaction would be to a man who requires "natural D-cup or larger only." Not great, I'd imagine.

I can do something about my weight, and I am.

Turned out I couldn't, so I stopped trying.

Can't do anything about my height.

Since then, I've seen pieces about some kind of surgery that puts extenders in your leg bones to make you taller. The surgery isn't risk-free, and from all accounts, it's painful with a fairly long recovery time. Not worth it, in my book.

We desperately need "accept yourself as you are" messages, but there's no money in that, so instead we're stuck with "you're just not good enough, but if you buy my crap, you'll finally be satisfied." (Spoiler alert: you'll never be satisfied.)

What's height got to do with anything besides blocking the people behind you in the theater?

I recently read an article in which some vapid lady expressed a desire to be "swept off her feet" both literally and physically, and apparently that could only be done by a 6'+ man? Okay, well, I wouldn't be interested in her, either.

I have to admit, as an aside, that I find it hard to see the whole "gender is a social construct" thing. I mean, yes, certain aspects of it are, in my view, but they're mostly superficial things: a particular style of haircut, wearing bigger watches (if one wears a watch at all these days), a lack of makeup.

Since then, I've come around more to to that point of view.

Basically, if something is a social construct, the social construct can be changed.

I stand by the "can be," but I recognize that those things take time, often longer than a human lifespan.

One of the greatest failings of modern society, I think, is this "binary" myth.

Standing by this statement, too. I've railed on binary thinking many times since then. And no, this isn't limited to the male/female binary; I think Netflix jumped the shark, for example, when it removed star ratings in favor of Siskel and Ebert style thumbs. But, lest anyone be confused by the entry's title, this sort of thing is what it referred to.

But still, my views have evolved somewhat. One thing, though, that I hope never changes about me:

And everyone deserves basic human dignity and rights (at least until they prove themselves unworthy of such by their actions), regardless of what pigeonhole you or society says they belong in.

I trust that's clear enough.

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