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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April 27, 2023 at 5:26pm

#1048899

Pushing My Buttons

It's going to be a short one today.

I decided to do one of my random road trips. Today, I ended up in White Sulphur Springs, West Virginia.

The only hotel in town (other than The Greenbrier, which is very expensive but you should definitely Google it because it's got a fascinating history) is conveniently located about a block away from the town's single brewery, Big Draft. I have already gone there to sample their wares, and they're very good.

This hotel - converted from a schoolhouse, because why would West Virginia need schoolhouses? - is less than a year old, so it's "smart." So smart, in fact, that when I checked in, they had to give me the user manual for the room controls.

Everything, and I mean everything, in the room is controlled by a touchscreen. The fucking toilet is controlled by a touchscreen. The icons on that touchscreen are incomprehensible, and they are NOT IN THE USER MANUAL.

And I'm not about to call the front desk and ask them how to use the goddamned toilet. Which has a bidet built in. While that's a great idea, again, the controls might as well be in French. Hell, if the controls were in French, I'd actually have a shot at understanding them.

Adding injury to insult, the room doesn't even have a desk. Which means I have to balance the laptop on a TV dinner stand. Which in turn means no mouse, and I hate using the touchpad. No, I'm not going to use my phone to blog; that's even worse. This is why I'm keeping this entry short, and not linking anything.

I hate this future. You remember the Daffy Duck cartoon where he's in a push-button house? Well, if you don't, Google that too because linking anything right now is a massive pain in the ass (unmitigated by the presence of a bidet and - I am absolutely, 100% not kidding here - the massage capabilities of the room's toilet seat). I thought it was funny when I was a kid. Not any more. I'm in a literal push-button hotel room.

The one bright spot in all of this, apart from the proximal brewery (which, again, is very good), is that the hotel has a bar. And I will be availing myself of its services shortly.

I just hope it's not staffed by robots.

8 Like • Comment • View 6 comments

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