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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Hey! Why are the signs at that Mac's in English if you're in France?

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WakeUpAndLive️~Happiness

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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

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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 1, 2023 at 10:07am

#1058428

Shorter Hops

Well, BBC, if you're trying to frighten me into once again giving a shit about climate change... congratulations.

Climate change could make beer taste worse

Imagine a clutter of hipsters squatting around a crackling campfire. Shadows flicker, unexplained lights glimmer from the inky depths of the surrounding forest. Engaged in the time-honored tradition of telling scary stories in the darkness, one of them holds a flashlight under his bearded face, casting unnatural shadows and highlighting where he'd forgotten to snip off a stray whisker strand.

He pauses in his tale, scanning the rapt audience until he's sure he has their undivided attention. "And then," he intones, "they discovered that all of their beer... had turned into Coors Light!"

Everyone: "Gasp!"

Yeah, they're hipsters, so they actually say "gasp" instead of gasping.

Anyway. I don't think this article is saying it'll be quite that bad, but it's scary enough:

Global warming is changing the quality and taste of beer, scientists have warned.

"Weather events will get more extreme." "Meh."

"Sea level will rise, inundating coastal cities." "Whatever; the people can move."

"We'll lose agricultural production." "So? It'll just relocate."

"Beer will taste worse." "Holy fuck, something needs to be done right now!"

Though I don't know if it'll really change any minds. We already know it's going to destroy chocolate and coffee production, and still not enough people care to do anything about it.

Hotter, longer and drier summers are predicted to worsen the situation, and could lead to beer becoming more expensive.

Beer always becomes more expensive. If it ever drops in price, they tax it to make up the difference.

Hops, the flower of the hop plant, are the crucial fourth ingredient in the beer brewing process - alongside water, yeast and malt. They are added before the boiling process to add bitterness, but can also be added afterwards to change the overall flavour.

Yeah, thanks, but no. I mean, yes, adding hops is important for flavor and aroma, but the reason we started with hops in the first place is that they're a preservative, and keep the beer from going bad as quickly. Especially important in the time before refrigeration, or after we stop producing electricity.

Farmers have been working to adapt their growing practices to improve yields, such as moving farms higher up valleys where there is more rainfall, and installing irrigation systems.

Irrigation systems are great, until their sources dry up, too. Which they will.

In summary, we're doomed, and we won't even have decent beer to drown our doominess in.

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