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🎶

about 22 hours 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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July 6, 2024 at 9:23am

#1073610

Down in the Valley

Might as well continue to discuss my travel plans on Saturdays. For now.

Nothing really changed this week. I'm supposed to meet with the travel agent on Wednesday, at which point I'll hopefully have a better idea of what I'll be doing.

The shifting political climate in France is a bit concerning, but it's hard to imagine it making them any more grumpy about American visitors. And I say "visitor" because that's how I prefer to think of myself, though, in this case, it'll be hard to make a case for that over "tourist."

If the situation does deteriorate, though, I might just concentrate on Belgium. Plenty of stuff I want to see (and drink) there.

From everything I've heard, the grumpiness is mostly a Paris thing, and it's not my plan to spend much, if any, time in that city. Though I'll schedule the visit to begin after the Olympics, I'm sure Parisians will have had their fill of tourists going in Seine.

(No. I will not get tired of that pun anytime soon.)

So let me tell you one thing I know I want to do (whether I'll actually get to do it or not is a different issue): spend some time in la Vallée de la Loire,

a region in western and central France.

The Loire valley may not be as well-known as Burgundy or Bordeaux, but it's a huge wine-making area. Other agriculture is prominent, too, from what I hear, but I don't care much about that bit. Specifically, I'm interested in Vouvray, which is a white wine (chenin blanc) that benefits greatly from the particular soil and climate of the valley. They export a few bottles to the US, and it's generally delicious; what I want to do is try the ones they selfishly keep to themselves.

Chenin blanc produced elsewhere is usually ass, but Vouvray is my favorite white wine.

There are also les chàteaux, which are usually interesting, historically and architecturally. Seeing castles is a remarkably touristy activity, but whatever. I did some of that in England and Wales, although the French castles are reportedly much better preserved.

I want to do other stuff, too, but a trip to the Loire valley has been on my fuck-it list for many years.

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