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!

about 6 hours 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

about 8 hours 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.

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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.

May 12, 2021 at 12:02am

#1010041

No Time to Morn

PROMPT May 12th

What TV show character would it be the most fun to change places with for a week? Why?

Well, the obvious choice is The Doctor (from Doctor Who). As a friend said, "Lives forever, controls his [or her] own destiny, has legions of fans." Obvious downside, though: that week is inevitably the one that the Daleks would choose to invade Earth, and I'd be too busy finding out if he has two livers as well as the famous two hearts to do anything about them, as Daleks don't drink. Plus the little matter of having "all of time and space" to choose from, and I'd be not only drinking, but suffering from decision paralysis.

So then I thought of Picard, from Star Trek. Commands the Federation's flagship, and women find him irresistible. But no, not only would I have to deal with the Borg and spotty writing, but I don't know if I could pull off being bald.

Besides, if I'm changing places, that means that either one of them would have to be me for a week, and then they'd have to hunt me down and destroy me.

Some superheroes come to mind, too, but see above about retaliation. This would be compounded if I picked, say, Raymond Reddington from The Blacklist. He's rich and cultured and has a private jet, so it would be fun for me -- until the week is over and he tracks me down and puts a bullet in my brain.

So, since I'm on the "Deep Space 9 / Voyager" phase of my long slog of a chronological Star Trek binge, I got to thinking about which of those characters I'd want to be, and I hit on the perfect solution.

Morn.

It's excusable if, even as a Trek fan, you don't know who that is, so I'll help out. He's a recurring character on DS9, a guy in full alien makeup that has a cameo in most, if not all, DS9 episodes. One of the most fun things about (re)watching DS9, which I haven't done since it came out and even then I missed a bunch of episodes because that was before streaming and partially after broadcast TV and I refused to get cable, was looking for Morn sightings.

They created this character, and did the whole alien suit thing, for (almost) every single episode as an in-joke. Dude doesn't even have one solitary line of dialogue. Morn spends all of his free time at Quark's Bar. I'm not even sure what his in-universe purpose is; probably something like moving cargo around in the station's many copious cargo bays, and the bar is where most of his cameos take place.

As a barfly in a busy space station, he gets to try every possible drink in the Federation - and beyond. The only downside would be having to deal with Quark, which is a character I find highly amusing on the show but who would be a real pain to actually interact with.

Best of all, from Morn's perspective, he wouldn't even have to change his lifestyle much while he's me. After all, I don't talk much, and I hang out at bars. He might even get over not having access to Romulan Ale or Klingon Bloodwine for a week, in exchange for trying many and varied craft beers. And I dunno, maybe I'd have time to leave my secret recipe for Romulan Ale in plain sight before the switch, along with all of the necessary ingredients. Well, actually, I already have those and I'm just waiting for the next Trek series to come out on Paramount+ so I have an excuse to mix up a batch.

Still, if I didn't have to concern myself with retaliation or alien invasion, I'd go with The Doctor. But Morn's still very high on the list.

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