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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January 26, 2021 at 12:22am

#1002873

Never Mind

PROMPT January 26th

Do you practice mindfulness or meditation? How often? On an average day, how often are you intentionally aware of your mental state and emotions?

Hm, let me just become aware of my emotions right now...

"Mindfulness."

I've made it a habit to rant against this "mindfulness" bullshit in here in the past. Here are some of the entries excoriating the nonsense:

Living in the present makes us less than human: "Brains"

Mindfulness isn't necessary for self-actualization: "Inspiration"

Mindfulness is snake oil: "Mind over Matter"

Mindfulness is incompatible with setting life goals: "Millionaire Blues"

It probably encourages complacency: "If You Don't Mindful"

"The Pursuit of Grumpiness"

Using mindfulness to cure depression can cause depression: "Animal, Vegetable, Mineral"

So you can see I've given "mindfulness" way more thought than it actually deserves, it being dangerous nonsense and all. It's just a way for charlatan New Age gurus to sell more New Age gurufiction by taking advantage of peoples' dissatisfaction with life. "Instead of actually changing things, I'll buy this book / watch this video and work on making myself complacent." It's the worst type of navel-gazing when what we need to do these days is to be focused more outward.

Oh, sure, people can seem to get something out of it at first, but the same could be said for any new way of thinking or viewing life.

As for meditation, well, if it works for you, fine. It annoys me when it's not actively putting me to sleep.

I feel like I'm always aware of my mental state or emotions. I may not always like what I become aware of, but it's like breathing: no one needs to tell you to "breathe." You're always breathing, or you'd be dead. Oh, sure, maybe you can improve on the way you breathe, but anything can always be improved. Similarly, you're always thinking, and you can train yourself to think better.

And do you really believe that someone whose entire purpose in life is to sell books and get paid to do seminars and shit is going to encourage people to think for themselves? People thinking independently is exactly what every huckster is afraid of.

So no, I don't buy into this horseshit.

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