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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Writer_Mike

about 8 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

1 Like

QPdoll

a day ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

a day ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:46am
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:16am
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

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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