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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 6 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 8 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

January 28, 2022 at 12:03am

#1025522

Control Alt Delete

A reminder: postings here will be at irregular times for the rest of the month due to an epic beer adventure upon which I am about to embark... weather permitting.

Meanwhile, one of the last few prompts from "JAFBG"

[XGC]:

If you could delete one website or tv channel from existence, which one would you delete and why?

Here is where I normally come up with an obvious joke answer, but to be honest, I don't want to.

For one thing, censorship sucks. "I don't like what you have to say, so I'm going to make sure no one else hears it." Sure, some censorship is unavoidable, because if you allow things like unrestricted ads or hate speech, things get ugly real quick and people will leave your site. But in my view, restricting what goes on in a forum that you control is a different matter than deciding that someone else's platform must be deleted.

I mean, age-restrict it, put up content warnings, whatever, that's fine; people should know something about what they're getting into. Banning something should be a last-ditch thing for truly despicable and/or illegal content (on the level of videos / photos of child abuse). Since I don't know any website or TV channel that portrays that, my answer is still "none."

For another thing, okay, let's say you don't agree with me (which is fine) and you decide to nuke... I don't know... Twitter. (Look, I understand. That was the one I was going to make the obvious joke about up there.) So you eliminate Twitter completely, dismantle its servers, send its administrators off to a gulag, and ban its corporate executives from going anywhere near a computer or a venture capitalist.

You do all that, and within a few months, there will be a new Twitter, run by different people.

If there's a demand for a service, someone will provide it. Eliminate Fox News? Something else will take its place. Pull the plug on Wikipedia? It'll take a while, but there will be a Wikipedia II at some point.

When there are both ethical and practical reasons for doing something (or in this case, not doing it), I'd say it's not worth doing (not worth... not doing... okay, whatever).

So, no, I can't answer the prompt because I wouldn't delete any website or TV channel from existence.

I sure as hell avoid a lot of them, though. Which if you don't like something, that's the way to go, instead of imposing your own standards on everyone else.

6 Like • Comment • View 3 comments

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