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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.




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June 23, 2020 at 12:31am
June 23, 2020 at 12:31am
#986319
Never had any interest in this activity. But it seems popular.

https://slate.com/human-interest/2018/12/real-estate-house-flipping-renovation.h...

Dismantling My Dreams, One Brick at a Time
We lived out our fantasy to flip a house. We will never do it again.


The sheer amount of work involved is mind-blowing. I mean, for that kind of time commitment and level of physical activity, you could mine for gold, or, you know, do pretty much anything else. Like write for Slate.

In the spring of 2016, my husband and I plunged headlong into one of the most tantalizing fantasies a couple can share: We bought a house to flip.

That is one of your "most tantalizing fantasies" with your husband? Flipping a house? Boy, I'm glad I'm not married to this chick. "Honey, should we do missionary position tonight, or just skip the whole ordeal?"

Okay, yes, I can accept the possibility that she was just going for humor. Still couldn't resist the sex joke.

Why did I want to flip a house? Well, who doesn’t?

*raises hand* Me! Me! I don't!

...the glut of home-transformation shows on TV prey on our fantasies that renovating a house can be an adventure, one that lets you escape the office, create a beautiful home for a deserving family, and earn a tidy pile of cash.

Okay, here's the thing.

I'm not entirely ignorant of the existence of these shows. I've seen them, occasionally, on screens at the gym in the Before Times, complete with closed captions so I had some idea of what the people were saying.

But did it ever occur to you, Ms. Brown, that there's a very, very good reason why these shows always focus on the joy that people take in tearing out walls, selecting fixtures, and (most importantly) collecting the money when someone else inevitably buys their fixed-upped house?

Could it be... oh, I don't know... the fact that 9 out of every 10 commercials on those shows are for home improvement stores, power tools, landscapers, real estate agents, brick suppliers, and the like?

Yes, I know the shows always also feature some sort of setback. "Oh no, this trim I bought is 1/4" too long! Whatever shall I do?" (Cue discordant music.) I mean, that's just Story Writing 101, right? Conflict generates interest. Said conflict is always resolved right after the next Lowe's commercial.

Lady, you've been bought and sold, and you didn't even know it.

To be fair, she does mention something like this setback moment, in different words, later in the article.

As lawyers working 100-hour weeks, we imagined buying some rough diamond, fixing it up ourselves, then displaying glorious before-and-after photos.

You're... both professionals... in high-paying jobs. Since you're lawyers, I'm going to go ahead and assume you're only actually working 50 hours a week and billing 100. Lawyers bill hundreds of dollars an hour. I could do the math, but you'd tune out. Suffice it to say that even low-end lawyers outside of the public defender's office make over $100K a year. Sometimes a LOT over. I can maybe see someone who's making min at McDonald's fantasizing about a fatter paycheck and not having to work for a clown, but come ON.

How wrong I was. Turns out the rest of the show, where things go well, is the fake part. Really, flipping a property is a montage of crisis moments.

That's in reference to the "setback" moment on those commercials. Yes, I consider the whole show to be a commercial.

The moment we drove up to our house—after the closing—we realized we had not paid enough attention to the house next door. Tiny brown bats circled its crumbling chimney. The place looked so haunted, I half expected hunched vultures to glare back at me.

Lady, you're doing vultures a disservice.

So we sold it. We made our target price, down to the dime. Doing so much of the labor ourselves, we made a reasonable, but hardly inspiring, return on our investment. Yet given the months of work and the financial risk we took, it was not worth it.

I've heard worse stories. Like people who thought they could get rich quick flipping houses before the housing crash in the late noughties, and got stuck with the resulting houses because they refused to budge on the selling price. Thing is? Such a crash could easily happen again. Sure, there's risk in everything, but it's one thing to take a risk on an $800 Beanie Baby and another thing entirely to take one on an $800,000 house.

It’s been two years, and we have no desire to flip another place. And we don’t watch those shows anymore.

I am glad you learned your lesson, young lady. There's way more money in class-action lawsuits. For the lawyers, that is. I might get 30 cents from the weaselly phone company for their deceptive billing practices, but you'll get $300,000.

*StarB* *StarB* *StarB*


Okay, so, great responses to yesterday's Urban Legend contest. Loved every answer, and I even learned about creepy things that I'd never heard of, and I live for this sort of thing. And the made-up one made me laugh because it demonstrates that someone's been following along. Thanks!

For whatever reason, the one about the haunted middle school worked best for me, perhaps because I could most easily see that one becoming the plot of a really bad exploitative horror flick. So this weeks' Merit Badge will go to... NaNoNette Author Icon! I'll send it out shortly. But again, I appreciated all of the comments, and you'll all have another chance soon!


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