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 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.

August 15, 2022 at 12:04am

#1036507

Labor

I've mentioned before that if you ask four economists a question, you'll get six answers. None of them will be right. If you want "right," you have to go to comedy sites like Cracked.

Nobody Ever "Wants" To Work, You Idiots

Okay, so not completely right. Plenty of people want to work, and would even if they'd be able to eat if they didn't. But I'm not one of those people, so I'll accept the title as hyperbole, not literalism.

An older generation disapproving of the incoming one is a tale as old as time.

I don't disapprove of the younger generation. I disapprove of every marketing gimmick assuming that they're the only ones that matter. Well, every marketing gimmick except ads for Depends. And even there, I'm not so sure.

The latest bug to crawl up the butt of the boomer generation is their collective decision, in what they’re calling “the Great Resignation,” is the idea that these ding-dang gosh-darn millennial snowflakes just simply don’t want to work anymore.

Considering that the youngest of what marketers have decided is the Boomer generation are pushing 60 right now, I know who doesn't want to work anymore, and it's the folks near or past retirement age. The definition of "retirement" is "not wanting to work anymore."

Instructor at University of Calgary and Twitter user Paul Fairie, smelling the stench of an argument endlessly made, put together a thread of quotes from publications going back a full century accusing workers of not wanting to work.

It's an image, so you'll have to go to the link above to look at it. In summary, it's variations of the phrase "no one wants to work anymore" in publications going back to the 19th century.

Once again, the people in need of labor for incredibly unrewarding jobs have pointed their finger at a willpower-less public. After all, they’re talking about fruit-picking, a job that is literally often used as a punchline or example of undesirable work. One that is now the go-to example of the work taken by desperate and less-than-documented migrant workers because, well, the job f**king sucks.

I can think of a few jobs I'd hate more than fruit-picking, but the point stands.

What’s even more bizarre about these froth-mouthed claims is that simple economic data doesn’t back up the narrative. The current unemployment rate in the U.S., via the Bureau of Labor Statistics, is 3.6%. This is one of the lowest unemployment rates in the last 50 years or more.

Mostly I'm including this quote because you're going to hear people claiming that unemployment is at an all-time high. Usually followed by "Vote for me in November."

I guess politicians want to work. Or at least provide the appearance of working.

So apparently, the amount of people that want to work is the highest it’s ever been, but no one wants to work anymore. How do these two things co-exist? It’s pretty simple: people don’t want to work TERRIBLE JOBS, and they don’t have to.

And as far as I'm concerned, this is great. There's a word for being forced to work a horrible job just so you don't die, and it was supposedly outlawed in the 19th century here in the US.

The unemployment rate shows that there is a large supply of jobs. If no one wants to work for you, that likely means whatever job you’re offering is in very low demand. So maybe do what the businessman you hold in such high regard would do in this kind of situation: examine why what you’re offering sucks so much that nobody wants it.

Of course, it's not always about the paycheck, or at least not just about that, but you know how people would say "I wouldn't do X for a million dollars?" Well, how about ten million? "Hm, I'll think about it."

Is paying your workers a living wage not financially viable? Well, unfortunately it seems like your genius business plan was actually financially unviable and was held afloat by simple desperation.

We can argue about what a living wage really means, but at the very least it means a single person being able to afford water, food, shelter, and electricity.

The words you’re looking for aren’t “nobody wants to work anymore,” they’re “I can’t find anyone desperate enough to do awful things.” Which, for anyone looking at a picture beyond numbers, isn’t the worst state of things.

It's not just "doing awful things." I derive immense satisfaction from stories about people quitting decent jobs because of shitty management. Because they can. Employers (remember, I used to be one) and managers have had the upper hand for far too long, and it's about time someone gave them a reality check.

By the way, the entire statement “no one wants to work anymore” is inherently dumb. Nobody likes to work, except for mattress testers and candy tasters. People work because it’s necessary to live and do the things in life that actually bring them joy.

This is the only part of the article I have an issue with. I know several people who, if they weren't somehow contributing something (aka working), would feel bad. Like I said, I'm not one of those people, but I know they exist. The open question is: would they take that job as a sanitation technician (second class) if they didn't need the money?

In conclusion, we're at the point right now where demand is high and supply is low. Classically, when that happens, prices go up to balance things. That's Econ 101, which I actually passed. The product in question, though, isn't bananas, but labor. And yes, this may be a cause of inflation in the short term, but in the long term, you have more people with more money they're willing to spend, and if production ramps up to compensate, things stabilize again.

If not, if inflation continues at an astonishing rate, then we've just proven what I've been saying all along: capitalism requires an underclass. Don't like it? Change the system. Not my problem anymore, because I don't want to work at solving it.

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