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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 2 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 4 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

January 24, 2023 at 12:02am

#1043587

AI See What You Did There

Lots of stuff about AI floating around. Cars, art, writing, etc.

It's not always a bad thing.

Artist Uses AI Surveillance Cameras to Identify Influencers Posing for Instagram
Dries Depoorter's "The Follower" project combines AI, open access cameras, and influencers to show behind the scenes of viral shots—without them knowing.

This article, from Vice, is fairly short, and I found it interesting, partly because of my photography background.

Dries Depoorter, the Belgium-based public speaker and artist behind the Die With Me chat app experiment, launched his latest project, The Follower, combining open access cameras and Instagram influencers.

On the other hand, I'm not a fan of precious artists.

Depoorter recorded weeks of footage from open access cameras, which observe public spaces, and which frequently have livestreams available online for anyone to access, that were trained on famous landmarks, including the Temple Bar in Dublin, Times Square, and the big sign at the entrance of Wrigley Field.

This part's important, because it emphasizes just how public this project is. It's not like he had to pull back much of a curtain.

The side-by-side comparisons between the casual-seeming photos the Instagram influencers chose to upload, and the footage of them laboring over the perfect way to hold a coffee, sling a jacket over their shoulder or kiss their date reveal how much work goes into a single photo for them—and how inauthentic the entire process really is behind the scenes.

As much as I loathe the entire concept of influenzas, and superficiality in general, I mean, that's a big part of what professional photography is: a lot of work. Sure, I spent a lot of time getting candid shots at parties, the kind of thing that anyone with a dumbphone can do now, but those are easy. Getting the right ligthing, the right pose, the right composition... that's work, and that's why professional photography is still a thing.

“If you check out all my work you can see I show the dangers of new technology,” Depoorter said.

I think the dangers are overreported. How about a project that exposes just how helpful some of this stuff is?

“I hope to reach a lot of people of making it really simple. I really don’t like difficult art. I like to keep it really simple. I think I’m part of a new generation of artists that work with technology.”

Everyone's hypocritical about something, but this juxtaposition—all within one paragraph of the original article—nearly broke my brain.

Capturing people in this way, unsuspecting yet fully public, feels like witnessing something intimate but also shameless.

Yeah, not really. To me, it feels like exposing the wires in a puppet show, or getting a tour of a clock tower, or watching one of those documentaries on the making of a Hollywood blockbuster: you see how the magic is done. That's not always a bad thing, either; once people know it's not effortless, perhaps they're less likely to feel inadequate by comparison.

It's like... you see your favorite celebrity, all slim and attractive, so maybe you feel like you got the short end of the beauty stick or something. But then you realize the amount of work that goes into that, and, okay, maybe it's not so natural after all. There still might be some feelings of inadequacy—in my case, I can't fathom doing that much work for anything—but at least you know there's more to it than just winning a genetic lottery.

It’s also a reminder that everywhere we go in the modern world, we’re being watched, even when we think we can curate and control what the world sees of us.

Isn't that what Elf on the Shelf is supposed to train your kids for?

4 Like • Comment • View 4 comments

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