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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10 Most Recent Blog Comments:

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

March 19, 2023 at 8:10am

#1046703

Revisited: "Speling Iz Dificult"

Today's random draw from the archives is from not so very long ago: October of 2021.

It concerned, as one might glean from the title, English spelling. "Speling Iz Dificult"

As it's less than two years old, the link is still there and, if you missed it the first time or want a reminder, here it is again.

In that entry, I noted:

I will say this, though: At some point, the spelling/pronunciation link becomes a shibboleth. I think people use it to identify in-groups. For example, in my area, there's a road with the name Rio Road. We use it to spot tourists. "Yeah, I hear (business) is on Ree-oh Road." Oh, they must be from out of town; the proper pronunciation is Rye-oh. Or there's a nearby town named Staunton. You hear someone pronounce it "stawn-ton" and you know they ain't from around here and need to be watched carefully and maybe lynched.

Weird story about that. Last week, I had to visit a dentist whose office is on a court just off Rio Road. It's on the other side of the city, but it's a small city. Nevertheless, I had Google Maps connected to my car's system (sorcery) so I could hopefully be aware of traffic and/or speed traps on the way there and back.

Anyway, the point is, as I was leaving, the Google voice went: "In five hundred feet, turn right onto Ree-oh Road." Annoyed because I'd just been to a dentist, I snarled, "Rye-oh!" A few seconds later, it reminded me: "Turn right onto Ree-oh Road." Not wanting to take anymore bullshit from a fake voice, I grunted, "Rye-oh!"

Then, after I made the suggested turn (really, the only other option was turning left), it said, "Stay on Rye-oh Road for a quarter of a mile."

I nearly crashed. Had it actually listened to me? Had it actually learned?

Another bit, not nearly as portentous:

Probably the worst offender in the orthography world, though, is the geoduck.

You see a word like that, and you think: oh, it must be gee-oh-duck. And it's probably a bird, right? An... earth bird? Well, obviously you're an ignorant rube and unworthy of respect because you didn't know it's pronounced "gooeyduck" and it's actually an enormous mollusk. How in the inconsistent hell do you get "gooey" from "geo?" I mean, seriously, goddamn, STOP IT.

I was remiss, then, in not noting that "geoduck" came to English from a PNW Native language. It's possible that the "geo" part was a word for genitals, which, if you look at the mollusk,

you might understand why. Nevertheless, there is no excuse whatsoever for spelling it like that. It's not like the Lushootseed language used Roman letters like English. Just do what you did with every other Native word, like Manhattan or Potomac, and fucking give it an English spelling closer to how it's pronounced.

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