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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Write_Mikey_Write!

about 6 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 8 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 30, 2022 at 12:18am

#1025659

The Fix

Only two left from "JAFBG"

[XGC]. After this, only one. Which I may or may not be able to post at the usual time.

Global supply chain issues. Is it a labor shortage, wage shortage, something else? How do we fix it?

Hell if I know.

I'm not even sure it needs to be "fixed." Not that it isn't inconvenient, but if we could fix everything that was inconvenient, we'd... you know, actually, that would be awesome. Get right on that.

I say that because these things tend to sort themselves out. Either we get shit moving again, or, if we don't, we get used to it.

As for the labor shortage / wage shortage thing... well, anything I say about that will be political. So I'm going to say it anyway: you want people to work, pay them more. If you want businesses to pay people more, don't be surprised when inflation happens. If people start getting paid better, and then inflation happens, don't be surprised when they end up being paid the same, adjusted for inflation, as they were before they got paid more. The system pretty much requires that some people be paid dogshit wages so the rest of us aren't inconvenienced. Don't like it? Change the system... or at least try not to be one of those getting dogshit wages.

Of course, it's not just about being paid more. It's also about not being treated like shit at work. I'm glad workers are finally starting to get the upper hand, because managers have become too complacent in thinking that they can do whatever they want and the peons will come to work anyway because they have no other choice. Well, now they have a choice. Just know that every time someone complains, "No one wants to work," what they're really saying is: "No one wants to work for me (because I'm an asshole)."

One thing I'm certain of, though, is the people who said that the exploited workers would come begging for their shit jobs back once stimulus ended were, obviously, completely wrong. Because it ended, and people are still not interested in working at your soul-deadening, productivity-optimized, unpredictable-schedule, doing-the-work-of-three-people, no-chance-for-promotion craphole business.

Don't get me wrong; I'd like to see the supply chain problems improve because I've been holding off on buying a car and a new laptop, both of which require computer chips that I hear are still in short supply. But I'm patient.

So far.

7 Like • Comment • View 4 comments

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