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

November 22, 2021 at 12:01am

#1022096

Powered Up

It's been said that everyone has a superpower.

PROMPT November 22^nd

You have found that you can do something no one else can do. What is this special talent you have? Would it be considered a 'Super Power'? If you could have chosen this special ability, what would it be?

Still, the idea that "no one else can do" what you do is farfetched. The world population is damn near 8 billion now, which is a number you can hear bandied around a lot, but we don't really have a grasp on it.

If you counted to 8 billion, one number per second, it would take you just over 250 years.

If someone describes you as "one in a million," then they're saying that there are 8,000 people just like you in the world.

Some few people manage to stand out, for whatever reason. Jeff Bezos' superpower seems to be amassing wealth (obviously, supervillains have powers too; I mean, shit, the guy even looks like Lex Luthor). But other people are almost as wealthy. I remember reading about someone who scaled Mount Everest without support oxygen. But other people can do that, too. Some free-divers can hold their breath for minutes -- again, not unique, even if there's one who holds the record. And those people who go ice swimming? Having anti-freeze in your veins is basically superhuman.

It's not unreasonable to believe that we all have some extraordinary quality or ability, but it is unreasonable to expect that no one else has the same power.

I had a friend who thought my superpower was punning. While true, I'm certainly not the only punster in the world, and yes, the others annoy me just as much as I annoy you. Besides, I make an effort to tone it down, like how Clark Kent has to tone down his handshakes so people don't find out he's Superman.

But I think my actual superpower is drinking.

Not quantity, though. A lot of other people can, and do, drink way more than I do, and I'm really not interested in competing at that, because I usually drink more for the taste than to achieve an altered state (that's just a side effect). No, my superpower is being able to drink multiple different drinks, in any order.

There's a saying people have: "Beer before liquor, never been sicker; liquor before beer, you're in the clear." I had to look it up just now, though, because I can never get it right -- and the reason I can never get it right is it doesn't apply to me. It's not that I never get sick or hung over; far from it. It's because the order in which I drink things appears to be irrelevant to the intensity of the effect.

Now, maybe the saying is bullshit in general; I don't know. It's possible that there's a psychosomatic effect involved, too, kind of like the placebo effect, where if you believe it, it becomes true. And as I said, I'm under no illusion that I'm the only one who can do this. But it's a useful talent, anyway.

Still. If I could have chosen a superpower, it would have been total recall. Not of life experiences; there are some I'm glad to have mostly forgotten. But of books, movies, music, etc. Many's the time I've remembered how much I liked or disliked a unit of entertainment, but when pressed, I couldn't come up with a single thing to support my reaction. It would be nice to be able to say more than just "Yeah, I read that, I don't remember what happened or who the characters were, but I didn't like it."

I know, I know, this is probably incompatible with the drinking thing, but as I already have two superpowers, it would be greedy of me to want three.

Or, you know. Being rich would be a nice superpower to have. I solemnly swear I'd use the money better than Bezos does.

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