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.

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').

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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.

3 Like

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

1 Like

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.

2 Like

March 1, 2023 at 1:26am

#1045737

Purrfectly Dark

And suddenly, March. I made it through February. Yay. This one wasn't as bad as most, but still not as great as the February I spent on Maui.

To celebrate, my final entry into this round of "Journalistic Intentions"

[18+], which features a cat prompt: Lounge

.

Ever notice that most black cats aren't black?

Not that there's anything wrong with that. It's just the way genetics interacts with kitty development. You almost always see a bit of white on a black cat: maybe the whiskers, maybe just a patch of tuxedo white on the chest. Even absent that, fur color depends in part on lighting. My cat Robin, for example, is so black that she blends into both my blanket and my mood. Cat camouflage. Sometimes you don't even see her unless she blinks, revealing the yellowish-brown eyes most black cats have (those come from the same source: melanin). Her nose is black. Her toe beans are black. Hell, even her whiskers are black.

Until you get her out into the glare of the accursed daystar, which is when you discover that okay, maybe she's not black; she's a very deep shade of brown.

Robin is also usually silent. Making no noise at all when she walks, she passes her stealth check every time. I think I've heard her meow twice, both times very quietly, in the seven or so years I've lived with her. Unless the lights are on, the only way I know she's there is I hear the double thump as she leaps off of some place she shouldn't be. But sometimes, yes, like most cats, she purrs.

Even Robin, though, has three fibers of white hair on her chest, as if to say "I'm not a black cat, really; I'm not." But being a cat person, I possess several statuettes of Bast, the Egyptian cat goddess, in her regal pose, like this one.

(I hope that link works). And Robin looks exactly like that when she's seated.

Thing is, though, cat fur color is only loosely correlated with cat behavior. While I've never had a calico that wasn't neurotic, I've heard that many of them are not. Contrary to popular belief, some orange tabbies are highly intelligent. Not all white cats are deaf, though the lack of melanin is sometimes associated with deafness. And black cats certainly aren't bad luck; they're just hard to see at night.

They're all just cats, and they're all different.

I can't remember ever choosing a cat, so it's not like I seek out certain breeds or coat patterns. Mostly, they were chosen for me, by parents or roommates or wives. Or the cat itself. But one day I'd like to adopt a mysterious raven-black tomcat, and name him Edgar Allan Purr.

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