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

March 6, 2021 at 12:03am

#1005891

You're Bad And You Should Feel Bad

Formula for annoying articles:

1) Pick something that everyone thinks is a good thing
2) Explain why that something is not a good thing

Like, say: 1) You may think you're helping the environment by recycling, 2) But in reality, the amount of energy used negates any benefit.

I don't know if that's true or not; I just pulled it out of my ass. But this one, I pulled off the internet from two years ago:

What Really Happens When You Donate Your Clothes—And Why It’s Bad
Blame fast fashion

And it only gets worse from there.

Cleaning out the closet for most millennials goes like this: You slough through the items you haven’t worn in the past couple of months or longer. Pack them into a tote you don’t need but keep around perhaps for moments like this. Sort the pieces you think you can get some money from at Buffalo Exchange or Beacon’s Closet if you live in New York City. Then, you bring the rest to your local Goodwill or Salvation Army and donate it.

Honestly, they lost me at "cleaning out the closet;" never mind that everything else in that paragraph is completely irrelevant to me. I have clothes from 25 years ago that I still wear. (Not underwear; shut up.) This idea that you have to get rid of shit you haven't used in two months is a pernicious lie meant to force you to spend more money to Buy More Stuff.

What actually happens to your donated clothes is a very involved process with a lot of complicated layers, each worth taking the time to understand. Let’s start here: Contrary to popular (naive) belief, less than 20 percent of clothing donations sent to charities are actually resold at those charities.

...and?

Almost half of the donations will be exported and sold in developing countries, while the other half will be recycled into rags and household insulation.

...AND??

The U.S. sends away over a billion pounds of used clothing per year, and a lot of those excess textiles are sent to East African countries like Kenya, Rwanda, and Uganda, each of which has received so much that some have proposed banning imported used clothing.

I'm still wrapping my head around the idea of not wearing an article of clothing until it wears out before getting rid of it as a rag.

To be fair, the article makes some mention of that later, but honestly, after this point, I just started skimming it. It doesn't help that their color choices absolutely suck, to say nothing of the implicit assumptions and writing style.

What you don’t want to do (ever, ever, ever) is throw away your clothes. You’ve probably already done that though, haven’t you? The average U.S. citizen throws away around 80 pounds of clothing and textiles annually.

Damn right I've done that. And I will continue to do that. Nowhere near 80 pounds a year, though. Not even close. No one is going to want to repurpose or recycle my used briefs.

Plus, at the end of the day, we’re the problem here. We’re the ones whose actions need to be questioned and challenged.

Because it's All Your Fault and You Should Be Ashamed of Yourself and It's In No Way The System's Fault.

No, "we" are not the problem, and "they" should stop trying to make us feel guilty about every goddamn little life choice. I swear it's all designed to keep us off-balance and neurotic so we'll be more susceptible to advertising.

6 Like • Comment • View 10 comments

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