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:

Write_Mikey_Write!

about 16 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 18 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.

March 29, 2020 at 12:06am

#979535

Doesn't Really Satisfy

Time to do entry #6 of 8 for

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts July 1!
#2213121 by Turkey DrumStik

Let's start by breaking down the description: Snickers S*per B*wl LIV commercial

1) Snickers
2) S*per B*wl
3) LIV
4) Commercial

1) Snickers. This is actually the least offensive thing to me on the list. If I wanted a candy bar, and there was nothing left available, I'd buy a Snickers rather than not have a candy bar. That's the best thing I can say about Snickers. I hate peanuts with an all-consuming, fiery passion and I almost wish I were allergic to them so I'd have an excuse to keep them the hell away from me.

I like peanut butter, though. Go figure.

2) S*per B*wl. I'm bleeping that out because the actual name of the game is copyrighted, and I don't want the lawyers (paid for out of nonprofit profits) coming after me. The last time I saw that game, it was when Springsteen did the halftime show. That was the only draw for me. I couldn't possibly care less about sports in general, or American football in particular. Know what I did last time that game came on? I went to Alamo to get drunk and watch the Groundhog Day movie. There were a lot of pissed-off employees there, because the movie started like an hour before the game did, and they all wanted to run home to see it. Yeah, the theater closed early that day just so employees could get their halftime commercial break fix. They were open on Christmas Day, but not S*per B*wl evening.

At this time, the Alamo is indefinitely closed, for obvious reasons. I wonder how many of them wish they'd spent the rest of February 2 making their wages & tips.

3) LIV. Know what I hate most about that game? The numbering system. Not the Roman numerals; I had those figured out in elementary school. It's that the first one was played the year I turned 1. That means that if you want to know how old I'm about to turn, translate the Big Game number into Indo/Arabic numerals, and there you have it. It's a constant reminder of my age, and I don't like it one bit.

Also, I was kinda pissed about 50. Every other one was numbered in Roman, but apparently they thought our puny little minds couldn't handle L, so they just called it 50. What will they do if they make it to 100? We'll C. Well, I won't. But some of you might.

4) Commercial. Eh. I've ranted about commercials in here before. I hate them with the fiery power of a billion merging black holes. I hate them so much, I've never had cable - the idea of paying upwards of $100 a month and still being subjected to goddamn ads made my blood boil. I'm fully aware that most people find them, at worst, mildly annoying, and I'm not trying to convert anyone to my point of view or make some grand statement about the evils of capitalism (hey, capitalism keeps me alive). It's just that whenever I hear "Oh, I don't care about the S*per B*wl; I just watch it for the commercials," my mind shatters into digital breakdown. I can't compute. I mean, I understand the urge to watch sports, even though I don't share it. That much makes sense to me. But ads are something to avoid, not look forward to.

These days, with streaming, I can avoid commercials, and it costs me less per month than cable. Granted, I don't have every streaming service out there -- notably, I skip Hulu because they like to charge AND show ads -- and I missed out on the whole Game of Thrones fad, which, after having the ending spoiled for me, I have to admit filled me with the warm glow of schadenfreude.

And finally, that particular commercial.

It... didn't age well, and it's less than two months old.

I admit it's pretty damn clever, though, and it pokes fun at a lot of the things that used to be wrong with the world before things we can't even see became what's wrong with the world.

And I do have to say that the ending had me

3 Like • Comment • View 2 comments

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