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!

a day 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

a day 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.

July 11, 2019 at 12:11am

#962433

Tattoo Vampire

Do you have any tattoos or want one in the future? If you had to have a piece of art permanently on your body, what would you want it to say about you?

No. No, I most certainly do not.

As I've mentioned numerous times, my dad was a sailor. Back in his day, pretty much the only people who got tattoos were sailors, whores, and circus geeks (not to be confused with science geeks, who may or may not have tattoos). While that's no longer the case, he managed to go his whole career and life without once getting the needle. He'd paraphrase Leviticus: "Thou shalt not put shit on thy skin."

More like LevitiCUSS, right, Dad? Told you: sailor.

I certainly don't put any stock in the customs or superstitions of Bronze Age goatherders, and I don't think people with tattoos (depending on their location) are any more or less worthy of respect or time. But as far as honoring my parents goes, the least I can do is follow his example on this one thing. No, I mean it's literally the least I can do.

That said, I'm not a fan at all. A tattoo is something I like someone in spite of, not because of. Or at least it doesn't factor into any dislike I might have (again, depending on the location - someone with a face tattoo is immediately suspect in my estimation).

I'm aware that, nowadays, most people have tattoos. A lot of them claim it's expressing their individuality. I express my individuality by not having any. And by wearing shaka shirts and Birkenstocks, but mostly by not having tattoos. "Hey, I express my individuality by doing what everyone else in my peer group is doing! Look at my tattoo!"

Don't get me wrong - I've seen some that are great art. That doesn't change the fact that I find the whole idea disgusting. I've seen great art in museums and on retaining walls, too.

If I were to change my mind - one thing that not having tattoos allows me the freedom to do at some point - I know what I'd want. A stylized sun, with the words "But Mama, that's where the fun is." Probably on my upper arm. But I'm not going to do it. There's really no need; anyone who knows me already knows I'm a Springsteen fan, and anyone who doesn't will probably get the wrong idea anyway - the more famous version of the song was a Manfred Mann cover with stupidly misheard lyrics - or they just won't care.

And that's the bottom line for me: I just don't care what you put on your skin. I care what's beneath it. Or I don't care at all.

I went down last night with a tattoo madam
To a nude dagger fantasy domain
Wrapped in hell, I lost my breath
Chest to stimulating Chinese breast

Grisly smiles, that don't flake off
Corny-colored demons leering
Vampire photos, sucking the skin

Seeding the night at the inker's parlor
Flash permabrand pricked for a dollar
Her wrist surreal a heart and flying skull
Lettered "Life and love pass swiftly"

Grisly smiles, that don't flake off
Corny-colored demons leering
Vampire photos, sucking the skin

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