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Sunday, Nov. 24, 2024

7:43am 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:

tj-turkey-jobble-jobble-hard-J

about 13 hours ago
In response to "Pursuit"

My grandmother used to say, "Pursuing happiness is like a dog chasing it's own tail."

2 Like

🌕 HuntersMoon

about 19 hours ago
In response to "Pursuit"

Happiness is reading your ramblings daily. True happiness is posting a snarky response.

3 Like

Robert Waltz

Nov 20, 2024 at 2:54pm
In response to "Powers of Three"

🌕 HuntersMoon

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

2 Like

Brandiwyn🎶

Nov 20, 2024 at 2:32pm
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

Nov 20, 2024 at 1:20pm
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

Nov 19, 2024 at 7:43pm
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!"

October 1, 2024 at 4:27am

#1077543

Lyon Sleeps Tonight

Another kind of slow day yesterday, partly because of another run on the TGV. This one took me from Dijon south to Lyon.

I should note here, as a bit of a warning to other Americans who want to visit France: while many people, especially in the travel and hospitality industry, speak some English, and many signs are multilingual, the vast majority of the train announcements and postings are solely in French. While I have some facility reading the language, it's not as easy for me to follow the spoken language (yet).

To be fair, I can barely understand train announcements in English. Ever been on the NYC subway system? The announcements there only add to the confusion.

The hotel that the travel agent arranged for me in Lyon is a step up from the others I've been in here. Five-star instead of three or four. For this particular hotel, part of the upscale amenities is a really remarkably well-stocked bar on the top floor.

Naturally, it became incredibly important for me to check out the bar.

And oh, man, was it worth it. While many of the spirits are also available in the US, they're a bit cheaper here. Even the Scotch, so it's not just because of the EU. The menu featured several interesting-looking cocktails, too, some of which I, of course, had to try. I was the only one sitting at the actual bar, and the bartender did the whole bartender-showing-off thing with the flipping behind his back and squirting drinks from an arm's length away and juggling shakers and all that. If I didn't know better, I'd think he was flirting with me. Or at least angling for a tip, which really isn't done here, from what I've been told.

They also have an 18-year Yamazaki (Japanese scotch-style whiskey), which I've had in the US, but only rarely. I restrained myself, though; I'll be here for a few days, and I'll have other opportunities to drink the really expensive stuff.

With all that, I haven't yet had much opportunity to explore Lyon, which is a really quite large city compared to all the others (except Paris). Today isn't looking good, either, with rain in the forecast, but I have a food-tasting tour lined up for later. That's for tomorrow's entry, though.

6 Like • Comment • View 2 comments

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