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Saturday, May. 4, 2024

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Kåre Enga in Montana

about 11 hours ago
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

about 16 hours ago
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

a day ago
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

July 4, 2020 at 12:14am

#987175

Forty

Happy boom-boom day, Americans! New rule: if I smell your barbecue, I'm coming over.

PROMPT July 4th

What could you give a 40-minute presentation on with absolutely no preparation?

One of my favorite scenes from TV is from a show I've never watched (apart from this scene). The only background you really need is that it aired shortly after Disney acquired Lucasfilm, and with it, the rights to Star Wars. So it's a bit dated now that the Skywalker Saga has officially ended, but taken in historical context, it's hilarious. Here it is:

Patton Oswalt is one of my favorite comedians, and he supposedly ad-libbed the whole monologue.

And yet... even though this guy is a professional actor and comic, and despite his impeccable geek cred, this cut clocks in at under nine minutes, part of which is intro. More, there are points at which he stumbles, backtracks, and even stutters. Now, I'm willing to admit that this might well have been all in character, but it doesn't come across that way. And still at the end of his roughly eight-minute filibuster, he practically collapses from dehydration and exhaustion (though I'm pretty sure that was a slice of ham).

As a bonus, you'll note Chris Pratt is in there, which adds to the awesomeness of this because he went on to join the Marvel Cinematic Universe, as I'm sure everyone knows, as Star-Lord ("Who?") in Guardians of the Galaxy.

I like to think Oswalt inspired at least some of Pratt's epic performance in those movies.

I, on the other hand, am not a professional actor, nor do I get paid for comedy (that's my free gift to the world; you're welcome). Okay, yes, I'm fairly well-versed in both Star Wars and the Marvel universe, but could I have done that?

No. Not without some preparation.

Now, I have done a bit of stand-up, but not for 40 minutes, and definitely not without rehearsal.

I used to know enough jokes to maybe fill 40 minutes, if I spoke slowly, but it wouldn't be original material. Besides, the internet has atrophied my formerly near-eidetic memory for jokes; why keep them banging around in my skull when I can google the punchlines and have the jokes right there in front of me?

Not to mention I'd have to make sure there were no kids in the room.

Hell, I once saw Lewis Black (another stand-up comedian and actor) when he performed in my town, and I had the honor of watching him utterly flub a joke on stage.

Of course, if you want the audience to fall asleep, I could probably have, at one point, given an ad-lib presentation on drainage design and erosion control practices in the Commonwealth of Virginia. But not these days.

On the other hand, I don't usually get stage fright, so that's something, I suppose. That trick you've heard about, the one where you imagine the audience naked? Doesn't work for me. It's supposed to make the speaker think that the audience is in an even more embarrassing situation than he or she is, I suppose. But all the blood flow to my brain ends up getting redirected.

I just realized that at least one of my teachers in high school must have used that trick. Sicko.

It's far more likely that knowing that I have to give a presentation will lead to those ubiquitous dreams where you're the one who has to perform naked.

As for Oswalt, after that show, he suffered some personal tragedy, but bounced back to work. And he eventually got to work for Disney/Marvel, as a side character -- well, several side characters -- in Marvel's Agents of S.H.I.E.L.D. We even got to see one of his characters sleeping in Star Wars bedsheets.

Good for him.

8 Like • Comment • View 7 comments

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