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Thursday, Nov. 21, 2024

4:05pm EST

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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:

Robert Waltz

a day ago
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

a day ago
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

a day ago
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

a day ago
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

Nov 19, 2024 at 4:04pm
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

3 Like

Brandiwyn🎶

Nov 18, 2024 at 11:27am
In response to "That's the Spirit"

Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success. Wow. Missed opportunity, here. How could you let this go without a shoutout to mighty Thor, son of the Allfather, wielder of Mjolnir, He with the Long Forehead? (Said in the voice of the Soup Nazi): "No Valhalla for YOU!"

Brandiwyn🎶

Nov 18, 2024 at 11:19am
In response to "Losing Weight Is Easy"

Has anyone ever told you how annoyingly pedantic you are?

Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless.

3 Like

tj-turkey-jobble-jobble-hard-J

Nov 17, 2024 at 4:04pm
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

October 3, 2024 at 12:09pm

#1077683

Beaujolais

The weather decided to give me a break, just in time for another wine tour out in the countryside.

Yesterday's excursion took me into the nearby wine region of Beaujolais, source of one of my personal traditions.

I've talked about it enough in here before, but, in brief: Beaujolais Nouveau is released on the third Thursday of November, just in time to ship it to the US for drinking with Thanksgiving meals, which it accompanies very well. I try to get a bottle every year.

This is not, of course, the only wine produced in the region, and their more traditional offerings are very good.

But the funny thing I found out on this trip is: the French consider it a trash wine. Which probably explains why the US gets so many bottles in November; they unload their stock on us so they don't have to drink it themselves. Every year when it's released on Beaujolais Nouveau Day,

though, they get together and party to drink the stuff and complain about how bad it is. And probably to laugh at the Americans who they can pass it off onto, but for some reason none of the tour guides I talked to would admit to that.

Thing about it, though, is the wine may be crap, but it's cheap crap, and to me, the price of the stuff figures into the taste. So yeah... I like it. Deal with it, France, because I have to deal with beer drinkers claiming to love Bud Light.

In other news, today is my last full day in France, but I'll talk more about today's events tomorrow, which is when I'm scheduled to get on a train to Belgium. I'm of the considered opinion that no trip to France is complete without at least one decadent, elegant, crazy expensive formal dinner. So I had mine last night, in the restaurant on the top floor of my hotel.

The only thing more boring than hearing about someone go on about their dream last night is hearing them talk about their decadent and crazy expensive French dinner, so I'll spare you most of the details, only to say it was everything I expected and not nearly as expensive as I thought it would be (and that neither snails nor frogs were involved). I accompanied it with a bottle of Pouilly-Fumé, which is not from this region, but what the hell, I like it and it was on the menu.

When I say bottle, I mean bottle. Damn right I polished it off.

Today's vacation photo was from an overlook where we stopped on the tour for a glass of wine. You will note that it's not raining, and that the view was incredible.

10 Like • Comment

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