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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Wordsmitty ✍️

about 6 hours ago
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

about 12 hours ago
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

about 13 hours ago
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

Lilli 🧿 ☕

about 14 hours ago
In response to "All Out of Louvre"

Have a wonderful time in France. Have you run into Annette in France yet? She's there too!

2 Like

Wordsmitty ✍️

a day ago
In response to "Bière Snob"

Great to see you got a good shot. And the picture is nice too.

1 Like

Writer_Mike

Sep 22, 2024 at 10:52pm
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

Sep 22, 2024 at 6:44am
In response to "Landmarks"

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

3 Like

Wordsmitty ✍️

Sep 22, 2024 at 3:41am
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

Sep 21, 2024 at 4:44pm
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Go Forth📖

Sep 21, 2024 at 12:51pm
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

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July 14, 2021 at 12:02am

#1013599

Rant Mode On

And another one for "JAFBG"

[XGC].

Tell us about something/someone that fucked you off this week.

Well. If we're only going back a week, I could talk about the rental car company, who overcharged me. Okay, they didn't really; it cost exactly what it said on the label. It's just that there were only two rental companies in town. You know them; they're the big names: Hertz, named after the electric shock you get when you see the bill, and Avis, which is French for "opinion" as in "in my opinion, Hertz sucks balls, but Avis is worse."

So, with no competition, they can charge whatever the hell they want to charge. And why is it that they make you bring the car back with a full tank of gas, forcing you to buy gas from the nearest station to the car lot, which inevitably has a 25% surcharge on fuel? Which is still better than the $6 a gallon they charge if you fail to fill the tank, but it's still robbery.

I rented the car on Monday but returned it Wednesday morning, so it's still technically less than 7 days ago as I write this.

Also on Wednesday, I flew home. Delta. Oh, I would love to rant about Delta... but the flights weren't all that bad, considering, and in a stark reversal from its usual policy, the Universe didn't hit me with a bunch of delays and cancellations that usually force me to find alternative means of transportation.

Still, airplane food, amirite? If only they still served booze on the flight. Makes me want to swear off flying forever, but there's no other way to get to Belgium next year.

Or I could complain about that perennial goblin, the DMV. Or BMV in some states, but here in Virginia it's the DMV. You all know the drill: in normal times, it's long lines and crowded waiting rooms. Bringing a copy of War & Peace won't cut it; you gotta bring the entire Wheel of Time series. Or, at least, that's what it would be if they still let people just wander in.

Let me back up. Because my car was totaled, I need to give the insurance company my title to the thing. Naturally, it's... somewhere. Who knows? So I need to get a replacement title. As such, I have two choices:

1) Make an appointment for seeing the one remaining employee at the DMV -- currently, there's nothing within 90 days, and they only schedule within 90 days. Or

2) Fill out a form online and wait up to 15 business days for them to mail me the replacement title.

Obviously, option 2 is marginally faster. Or would be if their website worked. Okay, to be fair, it probably works fine, but only if I turn off all the tracking prevention add-ons I have to slap onto my browser in order to have some measure of security.

If I don't find the title somewhere in my house today, probably under a pile of useless garbage, I'll try the online form with a different browser. As long as I only visit the DMV site, there's not much they can track, right?

But let's face it, the DMV is a too-easy target for rants.

How about my discovery that every car available right now for purchase, of which there are few, is overpriced?

I mean, this is not really a discovery. Supply chain issues, especially regarding computer chips, are well-documented. I knew this going in, but then, I wasn't expecting to have to replace my car this year so I figured, wait a couple more years and this shit will get sorted out. Well, I can go without a car for a while -- there was a period of six months last year when I didn't drive at all -- but eventually I'm going to have to suck it up and buy something.

But really, despite all this, I've had a pretty good week. I get groceries and beer delivered, and almost everything else I need is in walking distance. Which would be good for me if temperatures weren't in the 90s, but whatever; it's July in Virginia, and that shit happens, climate change or no climate change.

So, yeah, prompt or not, I don't mean to give the impression that life is some sort of slog. It's not. It's just that I can find something good and something bad in any given week, and for this prompt I kind of had to dredge something up.

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