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').

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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.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

September 16, 2019 at 12:02am

#966255

Athletic Non-Supporter

PROMPT September 16th

Another prompt from Elle - on hiatus

!

Have you ever played a sport? Were you any good? What did you like about it? Why did you stop playing (if you did)?

Not really, no, nothing, because I hated it.

There, done.

Okay, maybe not done. I'll just take this opportunity to rant.

I hate sports. I don't like watching them, and I especially don't like participating in them.

I'm not a competitive person. "But, Waltz, you're always entering contests here on Writing.Com! In fact, you're entering this into one right now!" Yeah, and winning is nice and all, but I don't enter them to be competitive with other people; I enter them to practice writing. Sure, I could do that without entering contests, but I tend to get more feedback by entering. And I can, to some extent, track my improvement. Most importantly, the only parts of my body that move are my fingers.

With sports, though, I hate everything about the things. I don't like physical activity. I don't like the risk of injury. I don't like how the other team, or individual players, try to psych you out. I don't like winning. I don't like losing. I'd rather simply not play.

Some things that may be considered sports aren't so bad. Bowling, for example. Not a lot of moving. Hard to injure yourself unless you overdo it or do something monumentally stupid like dropping the ball on your foot. You're mostly just trying to improve your own performance, unless you're in a league, which you don't have to be.

But I really, really hate being ranked. If you're near the bottom, people mock you. If you're in the middle, people taunt you. If you're at the top, people try to outdo you.

Goddamn primates.

And yeah, maybe I have lingering resentment over always being the smallest person in the class, and thus was always picked last for the teams, because everyone expected I'd be crap. Consequently, I was crap. I was a year behind everyone else, physically. Hasn't mattered for decades, but that shit stays with you.

Most sports are zero-sum games. One winner, one loser. There's no in-between. Oh, people talk a good game about "playing with heart" or "doing your best," but the only thing most people care about is winning.

It leads to the philosophy that life is all about competing. It's not. The basic process of society isn't competition, but cooperation. This is true even in sports - you focus on Team A vs. Team B, but there's an implicit cooperation even between the competitors; that is, the people involved agree on the rules first, and rule violations are penalized. But no one gives a shit about that; they only see the competitive aspect.

And I think that's fundamentally unhealthy.

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