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 15 hours ago
In response to "Landmarks"

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

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Wordsmitty ✍️

about 18 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

a day 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"

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WakeUpAndLive️~Happiness

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

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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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August 6, 2023 at 9:10am

#1053717

Revisited: "Finally!"

Today, we're going all the way back to 2008 for a prototype comment-on-an-external-link format blog entry: "Finally!"

It's short, but as the story is fifteen years old, it's no surprise that the link there is dead. No big deal; I could tell what it was about by the lede I'd copied:

SILVERTON, Ore. -- Management for a popular Silverton restaurant announced Thursday that young children would no longer be allowed into the establishment.

The manager at the Red Thai restaurant on Oak Street said children younger than 6 aren't welcome in the eatery.

Naturally, the questions, here in the future, are obvious: Is there still a Red Thai restaurant on Oak Street in Silverton, Oregon? And if so, is it under the same management? After all, even restaurants without controversial (but excellent) policies close down on a regular basis. Controversy might give them a temporary boost, but they'd have to keep generating more to get such free advertising.

A quick search revealed that, indeed, the Red Thai Room on Oak Street was, sadly, no longer in business. I can't be absolutely certain that "Red Thai Room" and the "Red Thai Restaurant" as mentioned in the news link are the same, but I'd bet money on it. My source? Yelp, which for some reason keeps records like that. There were only two reviews,

both from 2008, on the "recommended" page, both positive, but containing no mention of their wonderful policy.

What I found completely amusing was the dueling reviews on the "not recommended"

page: one one-star bitching about the no-brats rule, and another with five stars singing the praises of the no-brats rule.

Well. The former restaurant, now singing with the choir eternal, was, according to that Yelp page, located at 211 Oak Street. If the review dates are anything to go by, the restaurant, to my great sadness, didn't last long with its glorious policy.

But, if you're ever out that way, apparently there's another restaurant at that same address: Sandee Thai Restaurant.

What an amazing coincidence that the cuisine hasn't changed, but the name has.

Their food looks delicious, by the way, but I'm certainly biased as I love Thai food, or at least what passes for it in the US. The hotter the better. It generally requires some convincing them that, yes, even though I have pale skin, light hair and blue eyes, I love me some Thai spice; but usually, they acquiesce to my request. Though sometimes, they'll stand there with a carton of milk and watch me take the first few bites. Just in case.

I'm not ragging on people who don't tolerate spice well, incidentally. People like what they like. Only on the inherent racism of assuming that I'd be one of them, based on my looks.

And yes, I'm aware of the seeming contradiction between this and my desire not to eat around toddlers. Do not expect me to be consistent, but in this case, it's the difference between someone enjoying their meal in peace, or acting like zoo primates.

Back to my original entry, my words:

But it's nice to think about other restaurants, preferably ones in my area, following suit and denying entry to screaming kids. To me, there's little worse than being at a restaurant and having them seat a kid near me. Even when they're quiet, I end up losing my appetite when I see them eat. I'd rather be near smokers, or even loud drunks.

Sadly, the policy never caught on. Fortunately, my tolerance for the antics of young children in restaurants has increased since then, though if they try to seat me near one, I usually try to obtain a different table. Also fortunately, I'm far more likely, when I'm at home, to order takeout or delivery, thus avoiding both screaming kids and disbelief that a white guy likes his food Thai hot.

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