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.

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.

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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.

2 Like

August 4, 2024 at 10:31am

#1074760

Revisited: "NaNomaterials"

Today's peek into the past takes us back to September of 2018, and discusses a certain novel-writing month: "NaNomaterials"

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

I'm not really conflicted anymore; I just don't care enough to put in the necessary work.

I don't generally jump on bandwagons. If something becomes popular, I view it with a certain amount of distrust.

What's worse is that there are things I like that are popular. And I absolutely hate it when people assume that I like it because it's popular.

Yeah, I joined Facebook pretty early on, but I'm not active there anymore.

I can't even get into my account long enough to close it.

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.

Clearly, it's only gotten worse since that entry. It's not Twitter anymore, for starters, but X. Or, as I call it, Xitter (where the X is pronounced like sh). A post on the site is called a Xit (also sh).

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

I was hipster before it was cool. Then I stopped.

There follows a promotion for "October Novel Prep Challenge"

[13+], which I still recommend to anyone planning to do NaNo (or just want some help and motivation in getting a story together).

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.

Here it is six years later, and none of them have been edited yet.

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.

I spent so much effort world-building that last one that I've considered setting more serious fiction in that universe. "Considered" being the key word. The title of the entry was meant to be a pun on a science fiction trope, one which, like much SF, is entering consensus reality.

So why start something new when I can't finish what I've already got going?

On the other hand, if I can't finish what I've already got going, why not start something new?

Not this year, though. I expect to be traveling during October, and recovering during November.

5 Like • Comment

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