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 8 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 14 hours ago
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

about 15 hours ago
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

Lilli 🧿 ☕

about 16 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

1 Like

June 25, 2021 at 12:03am

#1012488

Outstanding

Entry #7 of 8 for "Journalistic Intentions"

[18+]

Insomnia is just another way to brand yourself "not normal". -Black Crisis

You know, something that's been percolating in the back of my mind for a while has to do with the tension between "being normal" and "standing out."

This generally peaks in high school and diminishes thereafter, but these days, I think it continues long into adulthood.

Clothing, hairstyles, activities... doesn't matter; lots of people walk the line between being too ordinary (and thus overlooked) and too weird (and thus dismissed as eccentric).

This is bad enough when you're actually in high school. There, you're among, at most, a couple of thousand teenagers (which, when put like that, makes me wonder how anyone has the stamina to be a teacher or school administrator). Like, my high school had around 1600 students, as I recall, roughly 400 in each class. With numbers like that it's not too hard to find ways to be noticed while still being accepted in a peer group.

Then maybe you get to college or trade school, and the numbers get larger, so you have to do more to excel at something. Fortunately, by then, the burning desire to "fit in" generally starts to recede. Still, there, depending on the school, you're competing for attention with several thousand other students.

But that was the old days.

Now, you have to walk that line not just for your immediate circles, but in competition with several billion people infesting the internet. Some people can do it through talent, looks, or smarts. For the rest of us, though, we're left with Stupid Human Tricks.

Or, for those who realize that Stupid Human Tricks can be dangerous, we have to find other ways to differentiate ourselves from the vast unwashed masses. For them, there's Munchausen's.

Now, I don't mean that to imply that people who talk about their various physical and/or psychological troubles are faking it. But even if it's real, it's a way to garner attention and sympathy, and to stand out from the crowd.

I'm not going to mention any examples here, because I'm not trying to offend anyone. But I will offer a counterexample: Chadwick Bosemen, who kept his cancer diagnosis to himself (and, presumably, some close friends sworn to secrecy). Of course, he had no need to seek out sympathy for attention; he was a talented actor. Those of us who don't get to be major movie stars, though, we have to take our attention where we can get it -- positive or negative.

And I don't want anyone thinking I'm ragging on them for this. It's just human nature, and I've talked about some of my own issues in here, too. Of course, we have to watch out for those few who do fake it to get sympathy. This usually takes three forms:

Munchausen's Syndrome: Faking (or exaggerating) illness for attention
Munchausen's-by-proxy: Faking illness in another person (often a child) for attention
Munchausen's-behind-proxies: Faking illness (in yourself or others) online for attention (and sometimes GoFundMe).

Okay, yes, I totally made that last one up. But I've seen it happen.

Of all of the possible ways to beg for attention, though (getting back to the original prompt quote there), insomnia is pretty tame compared to other things you can bitch about suffering. Most people have had it at least occasionally (myself included), so it's easy to sympathize. No one is going to think you're trying to scam them out of money by faking insomnia, not like with cancer or whatever. And it's not going to scare the unenlightened, like say talking about your schizophrenia.

Bottom line is, yes, it's hard to stand out in a crowded world. And maybe I should just give up trying.

Perhaps I'll sleep on it. Because I can. Because I don't have insomnia? Get it?

Oh, never mind. Even my so-called jokes don't make me "not normal."

3 Like • Comment • View 7 comments

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