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.

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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.

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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.

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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.

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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').

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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.

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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

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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.

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October 28, 2021 at 12:03am

#1020279

We'll See Who's the Total Moron

I really, really hate self-checkout at grocery stores.

The Banana Trick and Other Acts of Self-Checkout Thievery
“Anyone who pays for more than half of their stuff in self checkout is a total moron.”

But you know what I hate more than that? Well, I'm going to tell you anyway:

Thieves.

Beneath the bland veneer of supermarket automation lurks an ugly truth: There’s a lot of shoplifting going on in the self-scanning checkout lane.

Now, I understand that sometimes, theft is acceptable. Hell, sometimes it's even necessary because of systemic issues. But people who steal just because they can? Honestly, if it didn't disincentivize the thieves to leave their victims alive, I'd support the death penalty for it. Not just the death penalty; torture first.

That's how much I hate thieves.

Self-checkout theft has become so widespread that a whole lingo has sprung up to describe its tactics. Ringing up a T-bone ($13.99/lb) with a code for a cheap ($0.49/lb) variety of produce is “the banana trick.” If a can of Illy espresso leaves the conveyor belt without being scanned, that’s called “the pass around.” “The switcheroo” is more labor-intensive: Peel the sticker off something inexpensive and place it over the bar code of something pricey. Just make sure both items are about the same weight, to avoid triggering that pesky “unexpected item” alert in the bagging area.

I want to find everyone who does this and introduce them to Mister Pipe Wrench.

You're not stealing from the grocery store, you know. They're going to find ways to make a profit, regardless. Not much of one, but if they can't make a profit, they go out of business. When they go out of business, you get food deserts. And if they do find a way to make a profit in spite of these despicable assholes, how does it happen? That's right - by a) raising prices for the rest of us, b) keeping wages and benefits down for workers or c) both.

Either way, you're stealing from honest people and deserve to be flayed alive.

No, I'm not kidding.

The Leicester researchers concluded that the ease of theft is likely inspiring people who might not otherwise steal to do so. Rather than walk into a store intending to take something, a shopper might, at the end of a trip, decide that a discount is in order.

Stores could do more to prevent this sort of thing, but that too costs money. Eventually, you reach a point of diminishing returns, where the money you spend on security is more than the losses involved.

In their zeal to cut labor costs, the study said, supermarkets could be seen as having created “a crime-generating environment” that promotes profit “above social responsibility.”

And yes, that's a problem too. The worst thieves aren't even these checkout scammers; they're corporate assholes.

Whether out of social responsibility or frustration with shrinkage, some retailers, including Albertsons, Big Y Supermarket, Pavilions, and Vons, have scaled back or eliminated self-scanning, at least in some stores.

Which brings me to why I hate self-checkout in the first place. Well, there are lots of reasons, not the least of which is that it never actually saves time since some wage slave has to check my ID anyway because I'm inevitably buying beer and/or wine. But another reason is that it takes jobs away from people. It's not immigrants people should be raging at for "taking our jobs;" it's management's insistence upon automation.

“There is NO MORAL ISSUE with stealing from a store that forces you to use self checkout, period. THEY ARE CHARGING YOU TO WORK AT THEIR STORE.”

Bull. Shit.

“Shopping can be quite boring because it’s such a routine, and this is a way to make the routine more interesting. These can be risk-taking, stimulation-seeking people.”

And when they get caught, 20 to 30 years in Federal prison should give them all the thrills they'd ever seek.

No pity for such people. No tolerance whatsoever. Lock 'em up. I don't even care if it ends up costing society more in the long run; it's the principle of the matter.

...the problem being that because of the way society is set up, some people are forced into thievery, rather than just doing it for the thrill of the five-finger discount, and that is a systemic problem that needs to be addressed. But the court system isn't really set up to be able to tell the difference.

And I strenuously object to being called names for being honest. That alone is worth a few yards of duct tape and a pair of pliers.

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