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 15, 2023 at 9:29am

#1046411

Stupid Answer

Now, one from "JAFBG"

[XGC]:

What's the stupidest question you've ever been asked?

As tempted as I am to glibly answer, "This one," that would be both unfair and untrue. The problem is, out of all the stupid questions I've been asked, it would be very difficult to pick just one. Plus, my mind blanks on most of them. I selectively edit them out just like I edit out the stupid questions I've asked, except at 3 am when I lie awake going "Why did I ask that lady with the chihuahua if her dog was a Dachshund?" (Or whatever.) Everyone's mind blanks at some point, even mine.

I've never worked retail, though, so I suspect I've been spared the worst of the depths of derp. Things like pulling an item off of a display with a great big ALL ITEMS $4.99 sign above it, with $4.99 stamped on each instance of the item, and then turning to the nearest employee and going "Excuse me, how much is this?"

It's a good thing I don't work retail, because in such an instance, I'd be sorely tempted to go, "That? Oh, that's fifteen bucks, cash only, and I can help you with that."

Anyone smart enough to ask a question has enough intelligence to realize that they don't know everything, so I tend to be somewhat forgiving (believe it or not) of ordinary stupid questions. There are exceptions, though, like when someone asked me "Why isn't there a White History Month?" (If you need to know why that question is stupid, go Google it before asking me.)

Some questions seem stupid, but they're really attempts to strike up conversation. At the moment, though, I don't always recognize that, but then, like four weeks later, I'd be like, "Oh, they were just trying to find something to talk about."

Which leads me to what might well be the stupidest question I've ever been asked, which, in the grand scheme of things, really isn't all that stupid, but, like I said, I tend to blank these things out.

Scene: I'm in a senior facility visiting a friend's elderly grandmother who, while physically less than able, still had her mind, hearing, and vision. We'd stopped at a convenience store to get some things for her and also for us. One of the things I got for me was a bottle of Coke. Like, the trademark wasp-waisted bottle with the red label and distinctive cursive Coca-Cola logo in white. Absolutely unmistakable for anything else. I pull this thing out and take a slug.

And Friend's Grandma asks me, "Do you drink Coke?"

Before you pass it off as a "senior moment," like I said, this lady was sharp as nails, usually. If I'd been less stupid myself, I'd have answered something like "No, I just use it to clean battery terminals." But no, I was taken off guard by being asked if I drink Coke as I was sucking on a bottle of actual Coke. So I think I just nodded.

Again, though, it occurred to me like a week later that she was just trying to find an entry point to a conversation.

Such a thing, however, is the nature of some stupid questions, and if you can't tell the difference, there in the moment, between actual stupid questions and awkward overtures, well, then, who's really the stupid one?

4 Like • Comment • View 2 comments

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