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').

1 Like

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

1 Like

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 20, 2020 at 12:05am

#998739

Film Fest

What is this "post COVID" of which you speak?

PROMPT November 20th

It’s movie night at your place! Host a showing for your 30DBC friends of a movie of your choosing. Make sure the atmosphere is just right (imagine life post COVID

) As your guests arrive, how are they welcomed? Any pre movie activities or games? What are we snacking on? Have fun with this!

I used to have a ceiling-mounted projector.

Well, technically I still have it because disposing of electronics is nearly impossible (well... legally anyway). A while back, I had a leak that dripped directly onto the fucking projector when it had about 999 other square feet to choose from but no, it had to pick that ONE spot.

So, no projector. I still have the giant screen for it, though, and six speakers for surround-sound. So before I invite anyone over for movies, I need to fix the sheetrock ceiling (because right now I can't be arsed) and mount a new projector. I like those things way better than TV screens, and the projector screen is much bigger than any generally available flat-screen TV.

The one disadvantage is that if people get up and move around, it throws shadows on the screen. So don't do that. Once the movie starts, siddown and shaddup. I don't watch movies to socialize. I watch movies to watch movies.

We can socialize first, though, if you insist. ("How are [guests] welcomed?" With a hearty "Come in! We're downstairs! Drinks in the kitchen upstairs! Try not to scare the cats!") I bet you already know what the drinks will be. Go ahead. Guess. Worry not - there will be plenty of sodas and water for the abstainers. If you want coffee, though, you're going to have to figure it out for yourself; I don't drink it so I never learned to brew it.

As for snacks, well, I'm too lazy to prepare anything, so it'll be delivery pizza. None of that crap from Domiblow's or PooPoo John's though; the boxes those come in taste better than the pizza - I'm talking real, actual, pizza. And of course we can't have a movie without popcorn; that would be illegal. I suppose I could get off my arse and microwave some.

Before the movie, it might be fun to play a round or two of Cards Against Humanity. Nothing better to get to know someone than to test the depths of the darkness of their sense of humor.

Oh, you're probably wondering what movie we're going to watch. Well, when I used to have guests over, we usually watched comedies. Those seem to do best with crowds. But really, I'm flexible that way; we could watch an action movie. Or an action comedy. Or a comedy with action. See? Lots of choices! I'm a fan of consensus choice for movies. The projector is hooked up to the internet and I have Netflix and Amazon, so we'll probably spend more time deciding on a movie (and what toppings to get on the pizza) than we do actually watching the thing. (If we can't come to a consensus then by regal decree as the owner of the house, it'll be Young Frankenstein.)

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