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

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 27, 2023 at 12:01am

#1043725

Bizspeak

After a visit to the dentist, I'm on a course of antibiotics for a week because of a tooth thing. This means no drinking. 8 hours in. Send help.

Funny thing is, I go a week without drinking, no problem, quite often. It's only when they say I can't that my oppositional defiant disorder kicks in. Kind of like how I've never particularly enjoyed grapefruit, but as soon as I started taking a medication that forbids grapefruit, I started craving it. It's not even like I "can't" drink; it's just that alcohol negates the action of antibiotics, rendering them less effective (the precise opposite of what grapefruit does for statins).

Today's article has nothing to do with that, except that the subject matter is enough to make me want to drink more.

Let’s not circle back on that: These 10 corporate buzzwords are the most hated in America

“I’m just circling back to discuss how culture has changed within this new normal we’re in, hoping we can move the needle on this and think outside of the box.”

If I were playing the bizspeak drinking game, I'd already be passed out after that sentence.

But unlike talking about how it’s abnormally chilly out, no one really likes chatting in overused corporate phrases.

Apparently, many do. Mostly middle-management, I'd wager. It's been a long time since I was in an office setting, and even then it was a small office, and I still got subjected to the pin-putting and circling and such.

More than one in five workers dislikes corporate buzzwords...

See? The majority doesn't dislike buzzwords.

Below are the top 10 annoying phrases most hated among your coworkers:

You're damn right I have things to say about these.

1. New normal

This is probably a pandemic-related thing. Shit changes all the time, but the situation in early 2020 was more of a discontinuity than the usual gradual change.

2. Culture (e.g., “company culture”)

I'm not sure this is so bad as long as it's not overused [Narrator: it's overused].

3. Circle back

Pretty sure I remember hearing this one, and it annoyed me. The phrase that accompanied it was often "put it on the backburner," which annoyed me even more, especially when it referred to something I was working on.

4. Boots on the ground

There is no excuse for this unless you're literally fighting a war. And by "literally," I mean "literally."

5. Give 110%

I blame sports for this bullshit. The worst bizspeak, in my view, comes from sports. Even if this were physically possible, which it is not, are you going to pay me 10% more if I do this? No? Then I'm not going to do this.

6. Low-hanging fruit

As metaphors go, this one's not so terrible—unless it's overused [Narrator: ...sigh].

7. Win-win

Seriously, stop. Though it is nice to occasionally hear evidence that it's not a zero-sum game.

8. Move the needle

...once it's already jammed into your eye

9. Growth hacking

Okay, that's a new one for me, and it's legitimately enraging.

10. Think outside the box

The problem with the idea of thinking outside the box is that most people can't even think inside the box, which is a necessary first step. This is also known as "thinking." For example, say that your problem is you want to save money. The "thinking" solution is to find where you're spending too much money, and cut back. The corporate "thinking outside the box" solution might be to cut 1/3 of your workforce and make the other 2/3 do all their work without giving them raises. If you were really "thinking outside the box," though, you'd stop paying everyone and fuck off to Fiji.

Despite disliking buzzwords, three-fourths of respondents said that using these phrases can make someone sound more professional.

It certainly makes them sound more corporate.

But not all buzzwords are annoying. Preply respondents favored terms like “at the end of the day,” “debrief,” and even “sweep the floor.”

No, no, and no. Also no: "It is what it is." Make it all stop.

One in five respondents considered jargon in a job description to be a warning sign, with most noting that the language factored in their decision to apply or not.

You want to know what the biggest red flag is in a job description? I'll tell you. And it's not necessarily jargon. Here it is: "We consider ourselves family." If you see those words, or anything like them, in a job description, run. Run hard, run fast, and don't stop running until you hit an ocean. Then start swimming. Seriously. Every company that tells you they're "like family" is going to be just as dysfunctional as an actual family; or, perhaps, be an actual family that works well together—in which case you're going to be the Outsider and never quite fit in.

The main offenders for candidates were overly optimistic words that suggested an undercurrent of a more tense work environment, such as “rockstar,” “wear many hats,” and “thick skin.”

If you want me to be a rockstar, you'd better have the caterers ready to provide me with specialty cheeses and an olive bar. It's right there in my contract; didn't you read it?

This reminds me of the secret code of real estate listings, like "cozy" meaning "cramped," "private" meaning "in the middle of nowhere," or "vintage" meaning "draftier than a beer bar."

About the only positive thing I can say about these kinds of buzzwords is that they do make fine fodder for writing, especially writing antagonists. So it can be beneficial to learn them. Just remember, if you use them unironically, that means you're the bad guy.

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