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.

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').

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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.

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

1 Like

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.

2 Like

September 10, 2021 at 12:05am

#1017159

Rhetorical

Today, I have an article about writing... sort of.

21 Rhetorical Devices Explained

Even if you're not interested in writing essays, speeches, or other traditional vehicles for rhetoric, knowing the tools of the trade could be useful. If nothing else, it'll help you spot rhetorical tricks used to manipulate you. Maybe. Personally, I can never remember all the Greek-y words, but at least sometimes I can remember the devices they signify.

Rhetoric is often defined as “the art of language.” That might sound like a bit of a cliché (which it is), but it’s actually quite a nice way of saying that rhetorical devices and figures of speech can transform an ordinary piece of writing or an everyday conversation into something much more memorable, evocative, and enjoyable. Hundreds of different rhetorical techniques and turns of phrase have been identified and described over the centuries—of which the 21 listed here are only a fraction—but they’re all just as effective and just as useful when employed successfully.

I'm not going to hit all of them here. Just some comments.

1. ADYNATON

You’ll no doubt have heard of hyperbole, in which an over-exaggeration is used for rhetorical effect, like, “he’s as old as the hills,” “we died laughing,” or “hyperbole is the best thing ever.” But adynaton is a particular form of hyperbole in which an exaggeration is taken to a ridiculous and literally impossible extreme, like “when pigs fly!” or “when Hell freezes over!”

"When pigs fly" is one of my favorite phrases. I have a collection of winged pigs. Nothing profound about them; I just enjoy the absurdity.

Pretty sure Hell froze over when the Cubs won the World Series, though.

4. ANTHYPOPHORA

You know when you pose a question for dramatic effect and then immediately answer it yourself? That’s anthypophora.

Ha, I see what you did there.

5. ANTIMERIA

If you’ve ever friended or texted someone, emailed or DMed something, tabled a meeting or motorwayed your way across country, then you’ll be familiar with antimeria, a rhetorical device in which an existing word is used as if it were a different part of speech.

Verbing weirds language. -Calvin

9. ASTERISMOS

Right. Okay. Here goes. Asterismos is the use of a seemingly unnecessary word or phrase to introduce what you’re about to say. Semantically it’s fairly pointless to say something like “listen!” before you start talking to someone, because they are (or at least should be) already listening.

Yeah... I do use this one a lot.

17. HYPOCATASTASIS

When you say that something is like something else (“as busy as a bee”), that’s a simile. When you say that something actually is something else (“a heart of stone”) that’s a metaphor. But when you just go all out and label something as something that it actually isn’t (“You chicken!”), that’s a hypocatastasis.

I'm just leaving this one here because now hypocatastasis is my new favorite word. For now.

Anyway, like I said, just informational today. I wanted to have time to do a review. Yesterday I went to the theater and saw a... I don't know if "movie" is the right word. It's not a documentary. Whatever; I saw a film about the band Rush, focused on performances from their 2015 tour, with a few other fun things sprinkled in, and here's the review.

One-Sentence Movie Review: Rush: Cinema Strangiato - The Director's Cut

You can either accept that Rush was unique, and one of the greatest bands of all time, or you can be wrong.

Rating: 4.5/5

9 Like • Comment • View 4 comments

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