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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QPdoll

about 9 hours ago
In response to "Landmarks"

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

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Wordsmitty ✍️

about 12 hours 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.

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Annette in France

about 23 hours ago
In response to "Paris, I Guess"

Bienvenue en France.

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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

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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

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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

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WakeUpAndLive️~Happiness

a day ago
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/

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WakeUpAndLive️~Happiness

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

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

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Aiva Raine

a day ago
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.

Sum1's In Kalispell Montana

Sep 20, 2024 at 9:08am
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

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November 12, 2023 at 9:43am

#1059365

Revisited: "Real Men Don't Worry About..."

Another Sunday, another exhumation from the archives... though this one isn't buried that deeply; it's from early March of last year, featuring an article from six months prior: "Real Men Don't Worry About What a Real Man Is"

The link is from Cracked, so it's still around

as of today. I can't speak for how timely it still is; if you do the math above, you'll note that the article was from over two years ago, and things were... well, they were a little different in 2021. I don't follow trends closely enough to know if there's still a burgeoning "reclaim your manliness" industry, for instance.

As I've noted, one of the reasons I do these, apart from my blog rapidly running out of space and I'm trying to start to bring some sense of closure to it, is to see how my perspective or opinions might have changed in the intervening year or years (anything from before 12 months ago is fair game for these randomly-selected entries). But having re-read the entry, and the article, I'm not finding any notable evolution in my ideas on the subject.

I will highlight a few things, though:

Me: ...my body wash, which is also a shampoo, conditioner, salad dressing, cake icing, and engine lube.

I was quite proud of this line, and even received a positive comment about it. Hopefully, it's clear that it was a joke, but the reality is that my hair product is a) marketed to men and b) a "3-in-1 shampoo, conditioner, and body wash." Recently, it occurred to me that the cultural assumption still holds in the US that men have short hair, and that, more than sociological or biological factors, or even marketing, may be behind the labeling—though I imagine that it's attractive to many heterosexual men to have just one all-encompassing product to use, if only because their partners have taken up all the room in the shower caddy with their own various products.

Though I don't have that problem, I still appreciate its versatility and simplicity. Problem is, though, I haven't gotten a haircut since before the pandemic, and my mane was already fairly well-developed when all the barbershops and hairdressers temporarily shut down. At this point, it's pretty much full-on The Dude. While I'm glad I still have most of it at my age, I wondered (you know, one of those epiphanies you sometimes get in the shower) if I shouldn't look for something more designed for 80s-rock-star hair. But, you know, being men, long-haired hippie freaks and rock stars don't generally talk openly about hair care.

So here I am, talking openly about hair care. Because, as you might guess from the earlier entry's title, I don't worry about what a "real man" is.

Whatever; I'll keep using my all-in-one until it no longer works for me.

Another comment wondered why I didn't expand more on the final point made in the original article. I can't speak for my attitude at the time, any more than I can remember what I had for lunch that day, but upon re-reading that part of the article, I find I simply don't have much to add. I don't know what goes on in other men's heads any more than I know what my cat is thinking. The header includes the phrase: "Men Are Now Lonely, Isolated, And Scared"

Even if I agree, which I'm inclined to do, I don't have answers. Personally, I'm not lonely, even when I'm alone; I don't feel isolated, because I have friends; and apart from the occasional jump-shock from an unexpected indoor spider (they get relocated outdoors) or when I had to face eye surgery (which I came out of just fine), I don't live my life in fear.

If there's anything I could work up a comment on, it's this bit from the article:

If we insist on idealizing the '50s, maybe we should focus on the part where masculinity meant contributing to your community. That’s the real difference between men today and back then.

Guessing here that by "your community" they mean your physical location. Most of us have communities online, and they could be comprised of people from all over the world. For a time, as an example, I was gaming with a group that included someone remoting in from India, which is almost as far away as it's possible to get and still be on the same planet. And then there's this site, of course.

But in terms of local community, I don't have much of a presence. Yesterday, I made a brief and rare foray into the wild in order to attend a book discussion and signing by three of my favorite authors, all of whom live nearby—but I would never have known about their work if I hadn't found them online first.

Many years ago, I participated in a fantasy & science fiction book club, in person. Perhaps I need to find one of those again. Maybe find some decent shampoo, first.

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