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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Write_Mikey_Write!

about 21 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 23 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').

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.

January 6, 2020 at 12:12am

#972762

Spiders and Snakes

PROMPT January 6th

Write about something that makes you squeamish. What is icky, gross, or just plain “yuck!” Is there anything that makes other people shiver with disgust that doesn’t bother you?

Shit.

No, I'm not cursing (though I'm certainly not above that); I'm using the technical Anglic word for feces, scat, droppings, number two, etc.

You'd think, what with me being a civil engineer and having designed sanitary sewers and all, that it wouldn't bother me that much, but it does. I know most people are repulsed by it, but I think my aversion goes beyond the normal.

It's so bad that one of the main reasons I don't have a dog is that I'd have to walk it, which involves cleaning up its shit. Even touching the stuff through plastic makes my stomach churn.

I'm in no position to kink-shame, but if your "thing" involves scatology, we have nothing in common.

On the other paw, I'm not bothered by written descriptions of it. As a moderator here, I've read stuff that would make most people flee in holy terror. Doesn't bother me. Someone has to keep some of these interactives appropriately rated, and that someone is often me. As this particular blog is rated at 18+, I won't go into detail here.

So I'll talk about something else that seems to disgust other people that doesn't befoul me in the slightest: snakes.

I honestly don't know why some people are terrified of nope ropes. I mean, sure, some species are venomous. Still others have a painful but nonvenomous bite, but so do dogs and cats, and they're "cute." It doesn't take a whole lot of research to determine which slitherers are deserving of a wide berth. I'm still not disgusted by those varieties, but I respect them.

Spiders don't bother me much, either, unless one is crawling on me or looks like it's about to crawl on me. Or if they're huge. Still, they're not disgusting to me; they're quite beautiful from a distance. Unlike with snakes, though, I can understand others' aversion. All those eyes and legs, you know.

'I don't like spiders and snakes
And that ain't what it takes to love me
You fool, you fool
I don't like spiders and snakes
And that ain't what it takes to love me
Like I want to be loved by you'

7 Like • Comment • View 13 comments

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