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.

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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

March 20, 2023 at 9:48am

#1046731

Scorn on the Cob

Spring begins today! My local weather celebrates the occasion by being colder than it's been for a month.

Speaking of annoyances, another prompt from "JAFBG"

[XGC] today...

Share one 'hard limit' that would make you walk away from a relationship or friendship. Has that limit changed over time?

Let me answer the question before obeying the directive:

Yes. Yes, it has. And you might think that, as I get older and more desperate (in theory) for the kind of human connection that is denied to me due to my looks and personality, that I'd relax my standards a bit, but nothing could be further from the truth: I find I put up with less and less bullshit from people.

There are plenty of things I'll put up with in a friend, though, that I wouldn't want to deal with in a more intimate relationship. Veganism, or some other eating disorder, for example. If it's a friend, it doesn't affect me; eat what you want (if you try to claim moral high ground for it, though, we'll have a problem). But I'm not going to eat penance food, nor am I going to stop cooking meat-based dishes. Also, I'm pretty proud of my cooking, and would want to share it. The point being that it wouldn't make me any less a friend to someone, but that's all we'd be: friends.

So we need a dealbreaker that works for all kinds of relationships, and picking one is pretty obvious:

Being rude to service workers.

Now, obviously, all of us have bad days, sometimes. I'm not talking about the occasional snap. I mean a repeated pattern of treating cleaners, servers, receptionists, baristas, cashiers, bartenders, etc. (especially bartenders) like The Help.

Whether conscious or not, this kind of behavior is reflective of a hierarchical attitude: "some people are beneath me in social status and can be safely scorned; others are above me and must be appeased." So that's what I watch out for in potential friends: how they treat those of perceived lower social status.

And no, this doesn't lead to a virtue paradox: I don't think that rude people are beneath me; I just don't hang out with them if I can avoid it.

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