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.

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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.

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.

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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.

2 Like

April 7, 2023 at 1:27pm

#1047729

Sweater

Some of my entries this month are for "Journalistic Intentions"

[18+]. This one, for example.

Sweater

I've always disliked sweaters.

There's this vague recollection from when I was a kid and my mom called an article of clothing that her mother gave me a "sweater." I immediately hated it.

Not because the sweater was ugly—at that age, I couldn't have assessed its attractiveness, or lack thereof. Not because it was scratchy—which it was, but lots of the clothing I got foisted upon me back then was scratchy. No, it was because of the name.

Sweater.

Sweating, Kid Me reasoned to the extent of his limited abilities, is Bad. Why would I want to do something that's bad?

Now, half a century or so of not wearing sweaters later, because of this prompt, I got off my ass and actually looked into the etymology.

It didn't help.

As with many articles on Wikipedia, I walked away more, not less, confused.

From the extensive discussion of "sweater" on that site,

we get:

The OED gives "sweater" as appearing in 1882 and gives its definition as "A woolen vest or jersey worn in rowing or other athletic exercises, originally... to reduce one's weight; now commonly put on also before or after exercise to prevent taking cold. Hence a similar garment for general informal wear; a jumper or pullover"

You know what's an even worse name for an article of clothing than "sweater?"

Jumper.

Also jersey, but okay, I can see an English word for an article of clothing named after a place in the UK.

I'm not disrespecting the British here. Just saying that with "sweater," at least the word has at least some connection to what a person wearing it does. But "jumper?" Come on. Picture in your head a proper British person jumping. Can't do it, can you? Whether or not they're wearing a knitted or crocheted garment.

"Pullover" at least makes some sense. If you ignore the buttoned kind (usually called a "cardigan," and don't get me started on wtf that word might mean), one dons a sweater by pulling it over one's head.

But there are numerous other articles of clothing, notably t-shirts and sweatshirts (which are etymologically, but not fashionably, related to sweaters) that are also put on by pulling it over one's head.

French is no help, probably because there's a bit of cross-pollination between French and British English. You know what they call a sweater in France? It's not pronounced "sweat-ay" like you might expect. No, the French equivalent of a sweater is called a pull.

Just. Pull.

Meanwhile, the French word for the verb form of pull (at least the one relevant to this rant) is appuyer. Which is pronounced with an "ay" sound at the end.

Fashion words sometimes make no sense to me, and I've got seven more to do before the end of the month. Wish me luck.

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