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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June 25, 2024 at 7:57am

#1073156

Can't Spell Success without Sucs

Okay. Fine. Sometimes, clickbait works on me. It draws me in, fuels my outrage, makes me want to read more so I can rant about it..

Richard Branson says money isn't a good way to measure success: Focus on this 1 word instead, it's 'all that really matters'

Which is exactly the kind of thing I would say if I were a billionaire and the poors kept grumbling about dragging me and my head to a guillotine. It's like when they try to convince us that "money can't buy happiness" while they're flying in their private jets, smiling and sipping a gin and tonic made with low-paid laborer tears.

But let's hear this rich guy's take on it, anyway.

Richard Branson doesn't want to be defined by his money.

Well, you could give it all away and see how you're defined then. (Preferably, to me.)

"Maybe in America, 'billionaire' is a sign of success, but that rankles me," says Branson. "I think that your reputation is what you create."

Didn't his company declare bankruptcy recently? Oh, yeah, one of them did, last year.

Such success.

The company is largely responsible for his estimated net worth of $2.5 billion, according to Forbes — but he chafes at the idea he created it to make money.

Bet he wouldn't have done it if he didn't think it'd be profitable, though.

In fairness, $2.5 billion is small potatoes compared to people like Bezos or Musk, both of whom I mention because they're his direct competitors in the spaceflight field.

Of course, success is never guaranteed. If you do follow your passions, you'll still need factors like talent and perseverance on your side to avoid falling flat, experts say.

Mostly, though, you need luck.

And the real reason I decided to snark on this article? (In truth, I have nothing against Branson.) It's that the article ends with a promotion for one of its publisher's offerings, and the ad begins with the bolded phrase: Want to make extra money outside of your day job?

Still not sure if that constitutes irony or not, but I got a good laugh out of it.

Regardless, sure, success can only be defined by the individual. But having lots of money, no matter what problems it might bring with it, is always better than wondering how you're going to make rent next month.

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