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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Turkey DrumStik

about 11 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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.

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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.

3 Like

September 14, 2018 at 12:36am

#941387

NaNomaterials

Ever since I first heard of NaNoWriMo, I've been conflicted.

I don't generally jump on bandwagons. If something becomes popular, I view it with a certain amount of distrust. Yeah, I joined Facebook pretty early on, but I'm not active there anymore. And the first time I heard about Twitter, someone told me that some guy had rigged his office chair to tweet every time he farted. I swore then I would never be a Twat (or whatever they call people who go to Twitter), and nothing I've heard about Twitter since then has convinced me it's gotten any classier.

And no, this isn't some hipster thing for me. I won't join that group, either.

So I resisted NaNo for a while, but then "October Novel Prep Challenge"

[13+] came along, and I changed my mind.

Yeah, I promote the Prep a lot. No, I don't get paid to do it. Quite the opposite, in fact. So don't be thinking this is some sort of ad. Still, if one wishes to get one's thoughts together before tackling a novella in November (seriously, most published novels are longer than 50K words), it really does help. Point is, that activity gave me the motivation I needed to complete three works of fiction - and make a few attempts that went nowhere, but that's on me.

Anyway, I'm trying to decide whether to attempt it this year. Of the three I've completed, two of them are crying out for sequels (or, really, continuations to make them 100,000 word novels), and I've got a couple of ideas for new ones, though none are very compelling to me.

Of the three I've done, one's straight science fiction; one's contemporary fantasy; and the latest is, well, not a serious attempt at getting anything publishable done - it's science fiction erotica. Naturally, that's the one I most want to continue with, and it's the one least likely to get read.

On the other hand, all three of those are in serious need of editing and expanding - while my first drafts tend to be more coherent than most, they're light-years away from perfect. So why start something new when I can't finish what I've already got going?

So, I don't know. If I don't Prep, I won't NaNo, so I need to decide by the time Prep signups close on 10/3.

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