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

April 2, 2023 at 10:25am

#1047344

Revisited: "Judge, Mental"

In the course of picking, at random, an older blog entry to revisit, I ignore anything less than a year old. I figure it needs time to become vintage, and one year is generally enough for that on the internet.

Today, I got my first result from 2022—but it was from early January, so it's more than a year old. As it turns out, I do have something to say about it. The entry was mostly the answer to a former prompt from "JAFBG"

[XGC]; if you're following along, you know I've been working through the current iteration of prompts there.

As for the entry itself, here's the link: "Judge, Mental"

It starts off with a personal update:

Yesterday morning, we got a few inches of ugly, dense, watery sn*w which brought down branches, leaves, trees, and a nearby transformer (the electric kind, not the Michael Bay kind, though I did get to hear it explode). And my home generator picked yesterday to go on strike for higher wages and better working conditions. To be fair, any wage would be higher that what I'm paying it now, but come on, you only have to work like twice a year; get over yourself.

It took me several weeks, as I recall, to find someone to look at the generator. Fortunately, I didn't need it during that time. They did whatever they needed to do, and then, the next time the power went out... the generator failed again. Fortunately, that time wasn't during an intense cold snap.

I think it's finally back in shape, after I called out someone competent. Fortunately, or unfortunately (depending on your perception), it hasn't been fully tested under adverse field conditions, as this winter was mild.

If the power hadn't popped back on in the middle of the night, they'd have had to chip my corpsicle out of the solid block of ice that had once been a house.

I also have a vague recollection that, once I got the central heat working again that early morning, the thermometer on the thermostat said it had gotten all the way down to... 58F. Nowhere near literally freezing; just above, in fact, the ideal temperature for some darker beers and red wines. But enough for me to freeze my nads off.

In my last Comedy newsletter ("The Weather"

), I described with only a little bit of hyperbole how cold my dad kept the house, which you might think prepared me for a life comfortable with persistent hypothermia (my dad certainly thought, mistakenly, that it would toughen me up), but, in fact, the opposite became true.

Look, I live in Virginia. I expect this kind of shit at least once per winter. It doesn't mean I have to like it.

And this year, I found out what I like even less: not having to put up with "this kind of shit" all winter. I mean, sure, it was nice to have only a couple of sub-freezing days, and no sn*w to speak of, but it ain't natural.

Hell, there was an extended period over the winter where it got up to the 70s (F again, of course) during the days. That's warmer than it's expected to be today. Not entirely unusual for that to happen occasionally in a Virginia winter, but the lack of sn*w beyond a few non-sticking flurries was out of the ordinary. It's April, now, obviously, and it's been known to sn*w in April here; we'll see if we get any.

The rest of the entry doesn't really need embellishment; it's all about a thing I'm judgemental about: beer. About the only thing I can say is: I've been working on it, and I think I'm fairly successful in, if not being less judgemental about it, at least being less of a prick.

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