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.

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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.

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

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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.

2 Like

October 3, 2024 at 12:09pm

#1077683

Beaujolais

The weather decided to give me a break, just in time for another wine tour out in the countryside.

Yesterday's excursion took me into the nearby wine region of Beaujolais, source of one of my personal traditions.

I've talked about it enough in here before, but, in brief: Beaujolais Nouveau is released on the third Thursday of November, just in time to ship it to the US for drinking with Thanksgiving meals, which it accompanies very well. I try to get a bottle every year.

This is not, of course, the only wine produced in the region, and their more traditional offerings are very good.

But the funny thing I found out on this trip is: the French consider it a trash wine. Which probably explains why the US gets so many bottles in November; they unload their stock on us so they don't have to drink it themselves. Every year when it's released on Beaujolais Nouveau Day,

though, they get together and party to drink the stuff and complain about how bad it is. And probably to laugh at the Americans who they can pass it off onto, but for some reason none of the tour guides I talked to would admit to that.

Thing about it, though, is the wine may be crap, but it's cheap crap, and to me, the price of the stuff figures into the taste. So yeah... I like it. Deal with it, France, because I have to deal with beer drinkers claiming to love Bud Light.

In other news, today is my last full day in France, but I'll talk more about today's events tomorrow, which is when I'm scheduled to get on a train to Belgium. I'm of the considered opinion that no trip to France is complete without at least one decadent, elegant, crazy expensive formal dinner. So I had mine last night, in the restaurant on the top floor of my hotel.

The only thing more boring than hearing about someone go on about their dream last night is hearing them talk about their decadent and crazy expensive French dinner, so I'll spare you most of the details, only to say it was everything I expected and not nearly as expensive as I thought it would be (and that neither snails nor frogs were involved). I accompanied it with a bottle of Pouilly-Fumé, which is not from this region, but what the hell, I like it and it was on the menu.

When I say bottle, I mean bottle. Damn right I polished it off.

Today's vacation photo was from an overlook where we stopped on the tour for a glass of wine. You will note that it's not raining, and that the view was incredible.

10 Like • Comment

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