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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Brandiwyn🎶

a day ago
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.

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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.

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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.

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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.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

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January 7, 2021 at 12:01am

#1001590

You-niverse

PROMPT January 7th

What movie universe would be the best to live out the rest of your life in?

Oooh, good question. Haven't really thought about it. For me, fiction is fun but I don't imagine myself living there. So let's think about some of the more popular cinematic universes. Some of these might not meet the strict definition. I don't care. I figure if there's more than one movie (and/or TV show) that have continuity with each other, they count.

Marvel. This is the obvious choice, really, but it has major downsides, including the ever-present threat of godlike beings messing around with Earth. One could argue that this is what the heroes are for, but on the other hand, I'd hate to be between, say, Hulk and whatever Hulk wants to smash. So... pass.

Star Wars. Upside: Space travel, cool outfits. Downside: Ewoks, Sith, Space Fascists, and whateverthefuck JarJar was. Pass.

James Bond. Fun if you're an elegant, martini-swilling spy with cool gadgets. Not so much fun if said spy ever fails and some villain takes over the world. So, nope.

Harry Potter. You know, if you think about it, this might be the most ill-conceived universe after Twilight (which is itself a hard pass). So much of the "wizards are operating in secret" thing doesn't make logical sense unless you figure they're Jedi-mind-tricking everyone on a regular basis, and I don't want my mind messed with like that.

DC Extended Universe. Same problem as their traditional rival, Marvel, see above, with the added downside of really spotty writing. No.

The Matrix. Hell no. We have enough problems in our own world with people thinking we're living in a simulation.

John Wick. No. Hey, don't get me wrong; I love those movies but I wouldn't want to live in one.

Doctor Who. Only if I get to be a companion. All of time and space.

Star Trek. This one may be a bit of a cheat, since it's meant to be not an alternate universe but a future-us. And it started out as TV only, but more than enough movies have been made for it to count as a cinematic universe. And the upsides are plentiful: a post-scarcity society with warp drive, transporters, advanced medical science, and a unified humanity. So this is a real contender, for me. On the downside, though, you also have powerful aliens deciding to mess up Earth's day on a regular basis, just like in the MCU. I wouldn't mind living in the Trek universe. Preferably the original timeline, not the Kelvin one.

Also, coincidentally, on my current run-through of all the Star Trek episodes / films in chronological order of release, I'm approaching the end of Season 5 of TNG. One of the greatest Trek episodes -- hell, one of the greatest TV episodes -- of all time, in my opinion at least, was The Inner Light. In it, Picard, because of some alien technology, appears to experience the rest of his life on a different world (while he's passed out on the Bridge -- it makes sense in the context of the episode). I just had to mention this here because I was watching it when this prompt came up, and Picard actually got to do what we're talking about, albeit not of his own volition.

But I think the winner, for me, is the cinematic universe created by Kevin Smith: The View Askewniverse. It's a lot like our own universe, but with a lot more comedy and nerdy reference jokes.

Nootch.

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