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

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

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Wordsmitty ✍️

about 11 hours ago
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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

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WakeUpAndLive️~Happiness

a day ago
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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
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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 22, 2023 at 10:00am

#1059938

Drinksgiving

Today's entry isn't random, but inspired by "Invalid Item"

... today, the day before Thanksgiving in the US, and two days before Black Friday, we celebrate:

Blackout Wednesday

What's Blackout Wednesday? Well, you could just click on the link to find out. But for lazy folks:

Blackout Wednesday, sometimes referred to as Drinksgiving, takes place the night before Thanksgiving Day, and in some parts of the United States is one of the biggest drinking and party nights of the year. Many college students come back to their hometown for Thanksgiving, and go to bars the night before...

So, considering all the posts I do in here about fine fermented and/or distilled beverages, one might be forgiven for thinking that this is my kind of holiday.

It is not.

Not that I have any objections, mind. While I'm not above being a hypocrite, just like everyone else, I do make a conscious effort not to be. I remember college drinking culture (which probably means I didn't participate in it enough), and if I say I've never been blackout drunk, a condition I have labeled "danchu," which turned out to be a Mandarin Chinese word for "fade to black," as in a movie, I'd be lying.

I'm not above lying, either—I am, occasionally, a fiction writer—but I take drinking too seriously to deliberately make stuff up about it in nonfiction settings.

All of which is to say that I'm not judging anyone (unless they drive drunk, which I do get judgemental about), but Drinksgiving just isn't my thing.

There are several days on the official calendar—as opposed to the unofficial and mostly promotional calendar that I've linked to a few times this month, including today—that are devoted to drinking. These include such celebrations as St. Patrick's Day or Cinco de Mayo, as well as the more universal New Year's Eve.

I call them "amateur nights," and try to stay off the roads. Not because I'm drinking (necessarily), but because amateurs are.

And Drinksgiving is the ultimate Amateur Night; as the link demonstrates, it's all about college students (most of whom are still too young to drink legally in the US, but that's another issue and one I'm not getting into right now) coming home and drinking together. It's one thing to be a middle-aged occasional binge-drinker; it's quite another to have little to no experience with alcohol's effects.

Like I said, though, I was once one of those college students, so I understand, just like I understand why little kids play pretend or vroom model airplanes around.

Hell, I'm also a gamer, so I might even understand those things better.

It's widely known that with adulthood comes responsibility. While I, personally, avoid that as much as possible, college students are in that liminal space between other people being responsible for them, and them being responsible for themselves and others. Also, taste hasn't been altered by adulthood, yet, so there's less emphasis on what you're drinking than on simply getting danchu.

For instance, I had not yet developed my snobbery about drinking quality beverages; for my 21st birthday, I did 21 shots of Jose Cuervo, which is technically tequila in a way analogous to how Coors Light is technically beer—that is to say, it meets the arbitrary requirements, but still sucks.

As an aside, when I was in college, fermented beverages were legal for those 19 and older; they passed the law raising it to 21 on the day I turned 19 (and it didn't take effect until that July), so I was grandfathered in on beer and wine. Hence my 21st birthday hard liquor celebration.

I'm rambling, though, and I haven't even started drinking yet. My real point, here, is to dispel any misunderstandings about why I drink. Creating a really good beverage—that is, beer, wine, tequila, gin, or cocktail, e.g., is an art form, and I appreciate the art. Getting danchu is a bit like running a race through an art museum: you miss out on what is, to me, the best part of the experience, maybe glancing at the paintings and sculptures but without the time or inclination to really appreciate them, in favor of crossing that finish line.

I've noted before that many people, especially Americans (the only nationality I have great familiarity with, being one myself), don't have a middle ground. Either something is awesome, or it sucks. You either refrain from smoking weed, or you're a stoner. Either you're a teetotaler, or you're an alcoholic.

I reject that binary and live in the middle.

That is what I refer to as an alcohol-positive lifestyle: to acknowledge the downsides, while still enjoying the benefits. I guess that's part of the whole "responsibility" thing.

So, in brief, no, I won't be celebrating Drinksgiving or Blackout Wednesday or whatever you want to call it. But I'm also not going to rail against it. And I do have some fine craft beer to drink this afternoon... in moderation.

Not going to stop me from polishing off that entire bottle of Beaujolais Nouveau tomorrow, though. So in celebration of Thanksgiving, allow me to trot out my now-five-year-old Thanksgiving-themed poem:

Alcohol, Hookers, and Blow

(18+)
A Thanksgiving thanks giving
#2175291 by Waltz en France

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