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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Writer_Mike

31 minutes ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

QPdoll

about 17 hours ago
In response to "Landmarks"

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

2 Like

Wordsmitty ✍️

about 20 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.

2 Like

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

1 Like

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

1 Like

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

2 Like

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/

3 Like

WakeUpAndLive️~Happiness

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

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

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
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.

July 21, 2023 at 11:57am

#1052884

If You Cheese

I do like a "you're wrong about that" article... if the article itself isn't wrong.

Almost everything you know about cheese is wrong
Shredded cheese doesn’t melt as well and other fascinating facts about fromage.

Forcing French for funny fails.

A bag of pre-shredded cheese from the supermarket can really come in handy if you’re in a hurry and looking for a quick fix of salt and fat.

And you're not starting out stellar, here: cheese contains those things, but its purpose is protein. And, of course, flavor.

Unfortunately, many pre-shredded cheeses also come with a dose of cellulose, which is essentially wood pulp.

It's a nature-derived preservative. Would you prefer an "artificial" preservative?

The solution then is to grate the cheese fresh off the block or skip the grating process completely, says Mary Rizzo, owner of The Cheese Traveler shop in Albany, New York.

I mean, sure. But that's work. Not just the shredding part, but the cleanup afterwards. The convenience of pre-shredded cheese is enticing. If you banned shredded cheese, you'd Make America Grate Again.

Here are some other common fixes (or upgrades) you can make to your cheese game...

Shredded cheese snobbery is right up there with pre-chopped garlic snobbery, in my book. I admit it's better, but it's also often too much like work. Some of these other items, though...

Venture beyond processed cheese

Yeah, I've ragged on this in here before. Unfortunately, lots of people have come to believe that Kraft Singles is what cheese is "supposed" to taste like, or perhaps Velveeta, and there is no fixing that attitude.

Don’t always use air-tight plastic for storage

I have to agree with this one, too, but again, you have to balance the benefits with the extra work involved.

Learn why certain cheeses are crunchy

Because they're coated with nuts? Okay, no, the article explains this as a natural product of cheese aging. Which, admittedly, I didn't know the details of. So I learned something, too.

Sample real American cheese

I'm all for local artisanal food (I am, after all, a craft beer and local wine snob), but let's not limit ourselves to America, even if we live in the US. It is good to know that, according to this article, local cheese is finally happening in the US; I hadn't heard much about it.

Choose your pairings wisely

This is the kind of thing that can only come with experience, and perhaps someone else to act as Cheddi Master. Everyone's taste is different, even discounting the wrecked palate that leads some people to prefer process "cheese," and what works for me might not work for you.

But in the end, this is work that is worth it, to me: finding out which cheese pairs best with which wine or beer, or with other foods. It only improves one's enjoyment of life, and isn't that the whole point?

3 Like • Comment • View 1 comment

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