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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Annette in France

about an hour ago
In response to "All Out of Louvre"

I'm already out of Paris.

2 Like

Lilli 🧿 ☕

about 2 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!

1 Like

Wordsmitty ✍️

about 22 hours ago
In response to "Bière Snob"

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

1 Like

Writer_Mike

a day 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

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

1 Like

WakeUpAndLive️~Go Forth📖

Sep 21, 2024 at 12:25pm
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

Sep 21, 2024 at 7:34am
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

January 13, 2022 at 12:02am

#1024583

No One Wants To Work (Especially Me)

Well, this "JAFBG"

[XGC] prompt was going to come up sometime.

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

My city.

I can't say it was specifically this week. It's more of an ongoing thing.

First, a bit of background that's probably necessary for understanding:

Like many cities, mine has a recycling program. Whether the items that go into recycling are actually recycled or not is an open question, but that falls into the category of Not My Problem. Recycling is free (or paid for by taxes or whatever; the point is that we don't pay per pickup for recycling). Other waste (which I will refer to herein as Garbage to distinguish it from Recycling) is paid for through an annual fee and/or a per-pickup tag.

Garbage is picked up every week. Recycling is picked up every other week, by a different truck. In my neighborhood, we put the bins out on Monday evening for a Tuesday pickup, then we have to take the bins back from the curb by Tuesday evening.

I told you about the shitty sn*wstorm we had here last week. That was on Monday morning. I dutifully lugged the bins to the curb despite the sn*w. I didn't really expect the pickup to happen on Tuesday, because of the heaps of frozen slush, but just in case, there they were. Tuesday came and went. No pickup. Well, I'm not schlepping that shit back through the sn*w; probably it would happen Wednesday.

Wednesday goes by. No pickup. Most of the sn*w melted from the roads and yard.

I leave that crap out there (as do the neighbors) all week. No pickup. There's a Garbage bin, a Recycling bin, and several cardboard boxes filled with overflow recycling because I buy all kinds of shit online because I don't give a damn and it's not like I can go to stores right now.

The following Monday (this week, which makes this all fit the prompt), the garbage pickup happened. The recycling continues to sit by the curb. Getting soggy. There's no way in hell I'm dragging all of that back up to my house. I mean, it's only 25 feet, but now the yard is filled with fallen branches because sn*wstorm.

They're not going to pick it up this week. The next scheduled recycling pickup is this coming Tuesday.

Guess what's predicted to happen Sunday. Go ahead. Take a wild-ass guess.

You're right: a blizzard.

Well. A Virginia blizzard, which translates to "flurries" from the perspective of my friends in Minnesota, Michigan and Canada. Predictions are for a foot of sn*w. Or maybe mixed sn*w and ice. Or maybe rain and sn*w. Whatever, the point is, I'd bet $100 (the approximate annual price of an annual garbage can sticker) that the trucks won't make it here next Tuesday either, because this is Virginia and if there's a foot of sn*w, it might as well be twenty for all anyone can move on the roads. Meanwhile, I have another two weeks' worth of recycling ready to go to the curb. And to the curb it will go: on Saturday, before the oncoming storm, because there's no way in frozen hell I'm going to try to drag it through a foot of sn*w on Monday.

And if they don't pick it up, it will continue to sit there, because I'm done. I did what I was supposed to do. They did not. They can try to give me shit about it if they want, but the bottom line is: if they don't want a bunch of soggy, falling-apart cardboard boxes filled with a mix of more cardboard, plastic, beer bottles, paper, more plastic, cans, and more beer bottles, any one of which could fall apart at any moment, and which will soon be also weighed down by sn*w, sitting in the street, they can goddamned well pick it up themselves.

Not. My. Problem.

5 Like • Comment • View 7 comments

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