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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10 Most Recent Blog Comments:

Writer_Mike

about 13 hours 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.

1 Like

QPdoll

a day ago
In response to "Landmarks"

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

2 Like

Wordsmitty ✍️

a day 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.

1 Like

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

Sep 21, 2024 at 7:34am
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

Sep 21, 2024 at 6:46am
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

Sep 21, 2024 at 6:16am
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.

January 13, 2023 at 12:02am

#1043059

Kitchen Bitchin'

All of us eat, and someone cooks that, so hopefully something like this has some appeal.

15 Things I Wish Someone Had Told Me When I Started Cooking

I saved this article quite some time ago and I'm only now getting around to it. Consequently, I've forgotten what those 15 things were, so let's discover this together.

You know you’ve been in the food-writing world for too long when you’re shocked to see someone cut birthday cake with a knife…

How does this person not know to use a strand of taut dental floss or baker’s twine, which makes for the easiest, most mess-free slicing?

That right there is enough to ensure that I will always cut a cake with a knife. That is, when there is a cake. There usually isn't.

Sometimes I forget that not everyone is walking around with a mental catalog of time-saving, energy-saving, sanity-saving, life-saving, money-saving, surefire, guaranteed foolproof, plan-ahead, stress-free, problem-solving shortcuts, tips and tricks in the kitchen.

Apparently, we're doing everything wrong, including doing stuff wrong.

1. Don’t make recipes (or trust cookbooks) that have overly cutesy recipe titles like “Struttin’ Chicken.” These kinds of dishes rarely have the kind of staying power that a simple Roast Chicken will.

I agree with that on the grounds of cuteness, but my feeling? If you want to try it, try it. A recipe doesn't have to have "staying power" if it looks good to you.

Besides, at least the recipe isn't for "Cluckin' Chicken."

2. Buy yourself a pair of kitchen scissors.

Agree there, too, but how is it that this isn't basic? Even my mother had kitchen scissors, and she wasn't the world's greatest cook.

3. Some Type-A behaviors worth stealing: Do everything you can in advance when you are having people over for dinner. No matter how easy and tossed-off the task may be. No matter how many times your partner-in-crime says, Why don’t we just do that later? Filling the water pitcher takes 15 seconds!

While I object to the psychospeak of "Type-A behaviors" (though at least she didn't use the adjective "anal"), if a task takes 15 seconds, you can do it anytime. The problem is that you have a thousand 15-second tasks, which (math trigger warning here) is over 4 hours and 10 minutes. Sometimes, you have to prioritize; other times, task A needs to be done before task B, which needs to be done before task C, etc. If a task isn't on the critical path, move it around.

4. Brushing dough with a quick egg-wash is the secret to getting that shiny, lacquered, I’m-worth-something-after-all glow to your pies, breads, and galettes.

Fair enough, but that's baking advice, and I was looking for cooking advice. Baking is not my strong suit; I've never had any success with pies or breads, and furthermore, what the culinary fuck is a galette? No, I'm not going to be arsed to look it up.

5. Meat will never brown properly if you add it to the pan when it’s freezing cold and wet. It should be patted dry and room temperature.

I kind of feel like letting meat sit at room temperature is a great big no-no. I'm no expert at this sort of thing, but doesn't that just invite microbes to party? Especially ground meat. I've also heard that meat browns better if you add a bit of baking soda, but I've tried that and it didn't improve anything, in my opinion. Probably another attempt to sell more baking soda.

6. Add acid.

Sounds great! Oh, wait, they don't mean lysergic acid. Damn. Boring. (But true.) Also, fun if you do the baking soda trick.

7. Figure out the correct way to slice and dice an avocado. You will not only save time, energy and sanity by doing this, but you will find yourself giving tutorials to awed, in-the-dark observers every time you make guacamole in front of them.

I actually followed the link to the video in this one, even though I absolutely detest learning shit from videos. That may not be the worst way ever to deal with an avocado, but it's not the best, either.

Besides, if you're making guacamole, who cares what the cut-up avocado looks like? It's only going to get mashed anyway. I never make guac, though, and my slicing method may take a bit longer, but it gives me nice, clean, even avocado slices or dices every time. That is, if the avocado is in that fifteen-second window between "too hard" and "rotten."

No, I'd say "figure out the best way to dice an onion." Onions get used a lot more often than avocados, especially in my house, and I long ago perfected the quickest way to dice 'em up without getting blood everywhere. The only difficulty I have is peeling them; often, I give up and take the outer layer off along with the peel to keep myself from getting too frustrated to cook.

8. Ice in the cocktails, people. Fill that glass all the way up!

No. Just, no. Unless you really want a watered-down cocktail, or one that's more ice than booze. And some cocktails aren't served with ice at all. Martinis, e.g. Or single-malt scotch. Sure, some people like those on the rocks, but it's not a universal thing.

9. Learn how to make a handful of healthy dinners without using a recipe. Whether it’s scrambled eggs on toast or your great-grandmother’s 19-ingredient mole sauce, making dinner is so much more enjoyable when you can do it on autopilot, catching up with your kid or your partner as you go, or just savoring the aromas of sautéing leeks, instead of bobbing back and forth from cookbook to stovetop.

How is scrambled eggs on toast "dinner?" I mean, sure, it's fine to eat it anytime, but you're having breakfast for dinner. And who uses cookbooks directly anymore? Even if I do, I take a picture of the page or scan the text into my dumbphone. Keeps the cookbooks from getting messy. Phones are easier to clean than paper.

10. Compliment the cook. It doesn’t even matter if you don’t like the food! Someone took time from his or her day to plan, shop, and put together a meal for you to enjoy. Be exceedingly, absurdly grateful always.

Nevertheless: don't lie. Obviously give the cook a participation trophy; the work was the same whether the meal was tasty or disgusting, and that needs to be appreciated. But you're not doing your spouse (or whatever) any favors if they ask "how was the meatloaf?" and you answer "This was ambrosia of the gods!" when the truth is it tasted like sawdust and gypsum. I mean, you're not doing yourself any favors if you're brutally honest like that, but after a few days on the couch, they'll probably forgive you and figure out a way to fix the meatloaf. (The danger here is if they don't forgive you and next time they mix in actual sawdust and gypsum.)

11. A salad is not a salad without some sort of crunch

Oh, please.

12. Food trends come and go, but spaghetti and meatballs are forever.

I can't argue with that, but keep in mind that, 60 years ago, people thought aspics would be forever. (In fairness, there are probably still aspics around that were made 60 years ago, close enough to forever. Kind of like the family fruitcake.)

I'll skip the rest; you can go read them yourself. I don't think any of it is bad advice, exactly, but there's a lot of personal preference in there. And that's fine. I think we all have to do what works for us. The avocado thing, for example. Or maybe you like different things in salads than I do. Whatever.

The thing about articles like this is that a lot of cooking has to be figured out from experience. A recipe leaves out a lot of steps, by necessity: steps like "Pull the pan off the hook it's hanging on," because some people don't hang their pans. Or precise instructions for washing vegetables, which is also a matter of personal preference, space, and other factors.

Still, as with any other advice article, you take what works for you and leave the rest. Unlike with my mom's meatloaf, which was more "leave" than "take."

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