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:

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').

1 Like

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

1 Like

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

November 4, 2020 at 3:27pm

#997646

Run, Nose, Run!

No, I do not have a hangover; thanks for asking so loudly.

PROMPT November 4th

Details, details, details... Pick something in your view and describe it in as precise detail as possible without naming what the object is. See if you can get your readers to guess what object you're describing.

I did, however, wake up with a runny nose. This happens to me from time to time; while I'm not technically allergic to anything (except maybe an obscure ingredient in some protein bars), dust or pollen can irritate my sinuses just like with many actual humans.

But, of course, these days, a runny nose can be a death sentence, or worse, so my mind immediately leaped to: Could it be Trump-mumps? It feels just like every other time Nature has a good laugh at the expense of my mustache (it's hard to catch all the drips), but my best friend tested positive for Covfefe-19 the other day. Fortunately, she's basically on the other side of the country and I haven't seen her in person for months, so I couldn't have caught it from her. Still, that's where my mind went; it's 2020 and part of me would welcome the sweet release of death, but I'd prefer it not to take two weeks on a ventilator to get there. Anyway, I even took my temperature and, if anything, it's a bit low, I'm guessing from all the ethanol from last night that my system is currently frantically trying to process.

And yet, my nose is running like Niagara Falls, and it's annoying as hell.

All of this is to not only kvetch about it -- my blog, I can kvetch if I want -- but make the object from the prompt maybe easier to guess.

Its basic shape is a rectangular parallelepiped, which I can spell just fine but don't ask me to pronounce it. Wait, that won't help much, will it? It's a right rectangular prism, a rectangular cuboid... oh hell, it's a three-dimensional object with six rectangular faces, the parallel planes of which are congruent. The regularity of the container is broken by a large oval cutout in its cardboard. This morning, it was completely full of soft white pieces of flimsy paper, half of which are gone now because, at the risk of repeating myself, my nose absolutely will not stop running and no antihistamine or decongestant has ever done a goddamn thing for me.

The box is printed with artwork: stylized flowers. I'm pretty damn sure this is to make it so that people will buy more of these things faster, because we're highly suggestible, and what is one thing that triggers people with allergies? Flowers. That's what. It doesn't matter if the flowers are real or just pictures; hell, people have gone into sneezing fits just looking at oil paintings of flowers.

And the ones that don't have flowers on them? Grass. Ugh.

I guess they don't print them with pictures of ragweed because that would be too obvious.

So this thing's in my field of view, within easy arm's reach, and will remain so until Nature decides to stop messing with my head. Literally.

To make matters worse, I use a CPAP machine to sleep. If I don't use it, I don't sleep well, and I invariably wake up with a headache and a scratchy throat, not to mention everyone within five counties can hear me snoring. But if I do use it, it goes over only my nose. And right now, what's in my nose is desperately trying to escape, which makes wearing the damn mask that much more of a pain in the tuchis.

And yes, I know full well that lots of people have it worse than I do right now. That doesn't stop me from being irritated with the Fifth Horseman of the Apocalypse (his name is Minor Inconvenience; Famine, War, Death and Pestilence don't talk about him very much).

Chances are I'll do tomorrow's entry just after midnight, as usual. I couldn't do it last night because I was entirely drunk (as you have probably already intuited). But if I had, I would have missed the opportunity to describe this object and kvetch about my sinuses.

10 Like • Comment • View 6 comments

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