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.

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').

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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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January 6, 2021 at 4:04am

#1001532

For The Cause

PROMPT January 6th

Do you support any charitable organizations or causes through donations or volunteering? If so, what causes do you support? And if not, what would you support if you had the ability?

No. Not going to reveal that here. Not today.

I will, instead, list several things I will never willingly support under any circumstances.

The Salvation Army. Not only are they anti-freedom, but their people ring bells outside of grocery stores, and I want them to go away.

Any organization with the word "family" in their name. Without exception, these groups are Puritanical.

Religious causes. Although if a religious organization is doing actual helping work, I'd consider it.

Anyone with an overhead >10%. Though this rule is squishy, I want to make sure my donation is going to the cause, not the ad budget or organizer's private jet.

Any "children" charity. By which I mean any group where, when I'm buying something, the cashier asks me something like "Would you like to donate a dollar to X?" X in this case almost invariably has the word "children" in it, and all other such causes are tarnished by association. This may not be fair, but so be it. I will not put up with attempts to guilt me into giving spare change.

Spammers. Let's say I gave you $50 in 2001 because I thought your cause was justified. Over the course of the last 20 years, I have received 240 letters, 1,040 emails, and numerous phone calls / texts from you. The total cost of delivering said barrage of beg has far exceeded the $50 I gave you then, so you're not getting so much as a penny from me ever again.

Solicitors. Show up at my door? Fuck off forever.

Anyone that uses a baby animal (including human) image in their solicitation. Your emotional blackmail will not work on me and will, in fact, have the opposite effect.

All this, as you might imagine, leaves me with only a few options, but I am still reluctant to discuss them. I generally prefer to keep this sort of thing to myself, though get me drunk enough and I'll probably confess. I'm not drunk enough now (though it's not for lack of trying). It's just not anyone else's business. I know that's an odd thing to say after I've shared so many other things in here... but that's just the way it is.

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