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Saturday, Nov. 16, 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:

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').

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.

September 28, 2024 at 2:17am

#1077370

To the East

Most of yesterday was taken up by traveling. To get from Tours to Dijon, apparently there's no direct way, or at least not one that gave kickbacks to my travel agent. So it started with me taking an Uber from my hotel to the Tours train station, because now I know better than to roll luggage for that mile. Then the TGV back to Paris, during which, for some reason I absolutely cannot comprehend, my assigned seat was right next to someone else... while there were maybe 2 other people in the entire car.

But the real fun was when I got back to Paris and met the chauffeur for the ride from Gare Montparnasse across the Seine to Gare de l'Est, which is the station with the train to Dijon. The chauffeur didn't speak very good English or French, but he spoke excellent Ukrainian. At least I assume he did; I know almost nothing about that language. But he was very good at pointing out the Paris sights along the way, in some version of English with a Ukrainian accent.

"There is Tour Eiffel. And this building on left?" He indicated one with scaffolding. "Ukrainian mob has construction contract." We drove a bit further. "There on right is Notre Dame. And over there, building by Ukrainian mob." I wanted to ask him if the mob also did the Notre Dame reconstruction, but I knew better. He pointed out other important Ukrainian construction jobs along the way, too.

Now, look. It's entirely possible that "mob" was a bad translation of something else in Ukrainian. Something innocuous like "Fine Upstanding Ukrainian Construction And Renovation Company And Not Mob At All We Promise And Pinky Swear." But I choose to believe that my chauffeur, who was about my age, was an actual member of the actual Ukrainian mob and did the chauffeur thing as a day gig.

Just in case, I gave him an enormous gratuity.

As Skinny Pete said in The Italian Job, "If there's one thing I know, it's never to mess with mother nature, mother-in-laws, and mother-freaking Ukrainians."

After that, the train (the slow kind) to Dijon was a letdown. Hell, the rest of the trip might well be a letdown.

Things picked up again, though, once in Mustard City. The hotel, this time, is like 100 meters from the station. It has a lovely little bar. I had dinner elsewhere, but came back for the bar, where I got acquainted, for the first time, with a regional (the east of France) custom: Picon bière.

Mostly, they drink Belgians here, because, as I've said numerous times, traditional French beer is ass (also, it's wine country). But apparently, it's not flavorful enough for them (QUOI?!) so they add a shot of a kind of orange bitters called, you guessed it, Picon.

And whaddayaknow, it's actually a pretty good combination. Sadly, Picon isn't generally available in the US, so I'll have to enjoy it while I'm here and then smugly brag about it every time I drink a Belgian beer back home.

8 Like • Comment • View 1 comment

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