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?

With all that walking, I hope you stayed hydrated.

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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

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
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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 13, 2023 at 9:53am

#1059420

Secrets Revealed

Every once in a while, I run across something I didn't know about. Weird, huh? That I don't know something? Well, now I do.

A Secretive Food Culture Enters the Spotlight
Peranakan cuisine is a feast of complexity

I'd never heard of the culture, let alone the food. Obviously, I've never tried it. Honestly, Atlas Obscura, here, could have made this whole thing up, April Fools style, and the joke would have been lost on me. Naturally, I checked out the Wikipedia

page, with the understanding that those can be a spoof too. But nope... just an entire culture I'd never even heard of.

Jiu hoo char is a specialty of the Peranakans, a cultural group that stretches across Malaysia, Singapore, and Indonesia. While not Peranakan herself, my mother inherited her jiu hoo char recipe from my grandmother, who inherited it from my great-grandmother, who in turn learned it from her neighbor, herself a nyonya—a Malay and Indonesian honorific for married women of the Peranakan culture.

Somehow I doubt that these recipes translate well into Western standard cookbook recipes. But I don't know; maybe someone's tried.

As recently as a decade ago, there were fears that Peranakan cuisine might die out, due to the tradition of recipes passing only from mother to daughter.

Based on what I saw on the Wiki page, it's not just the cuisine but the culture itself that seems to be hovering on the edge of decline.

Just off New York City’s Union Square, Kebaya is the first restaurant in the city to focus on Peranakan food.

If there was going to be one anywhere in the US, I'd guess New York or Los Angeles. I visit New York fairly often; this is something I'd like to try.

Peranakan culture dates back to the 15th century. Derived from the Malay word anak, meaning child, Peranakan refers to the descendants of the Chinese seafaring traders who landed in Southeast Asia and married local Malay women. Today, pockets of Peranakan culture are scattered across Indonesia, Singapore, and the Malaysian states of Penang and Malacca.

I don't know enough to tell whether there's bigotry involved. We in the US don't have a monopoly on racism.

A key hallmark is how much care goes into each dish’s preparation. Take kuih pai tee, for example, a petite vegetable-and-spice filled pastry. Making the tart shells requires dipping a mold into a thin batter, and then dipping it into a hot vat of oil and removing it at just the right moment. Remove it too soon, and the shell crumples; leave it in too long, and it burns.

Yeah, that's a lot of finicky work.

Below are some of the unique building blocks that make up Peranakan food.

I won't go into this part. For once, though, I'm not put off by the graduate thesis food bloggers always write before getting to the practical part. I'm a little bit less ignorant than I was before I read the article, and that's a good thing.

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