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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Show Recent Comments

February 25, 2022 at 12:10am

#1027390

Hot Tip

It's been a while since I've ragged on tipping articles. Sadly, I don't have a lot of time today because I'll be getting on a plane later. Hopefully I won't have to tip the pilot.

Our Easy Tipping Etiquette Guide Tells You How Much to Tip in Every Situation
From manicurists to movers and beyond, we've got you covered.

Unfortunately, the solution doesn't seem to be "go live in a sane country that doesn't require tipping."

According to Swann, the word "tip" was first used as an acronym for "to insure prompt service" in the early 17th century, when ladies commonly took tea in gardens. With the kitchen so far from the table, lukewarm tea was a problem—at least until clever guests began leaving coins to encourage servants to bring their hot water more quickly. The practice thrived and spread, becoming standard in many parts of the world.

And with that, we know we can safely ignore anything else the article has to say. That particular bit of backronymage has been so completely and thoroughly debunked that anyone writing an article on tipping should have immediately known it was bullshit.

Worse, this Swann person is presented as an "etiquette expert." While that doesn't translate to "language expert," if you present yourself as an expert on tipping and you don't know the really quite very simple fact that TIPS did not start out as an acronym (neither did shit or fuck, by the way), then nothing else you can say can be believed.

But I'm going to excerpt some things from the article anyway, and it turns out that even a stopped clock is right twice a day. There's a bunch I'm leaving out because, as I said, not a lot of time today.

There are a few exceptions to the tipping rule, like baristas or people working in sandwich shops, who as Swann notes, are making an hourly wage. "Most importantly, those tip jars are something that business owners have created to share with their staff members as a perk," Swann says. "You are not required to tip them, although if they have gone above and beyond—maybe you had a large order, or had a situation that was very complicated—then you are welcome to extend your graciousness by giving a tip."

This is probably going to get me some hate mail, but I agree with the first part. The first time I saw a tip jar at a coffee shop (I do go to them sometimes to socialize and maybe get a tea), I nearly lost my shit. "Wait. You want me to stand in line, give you my order, pay in advance at the counter, wait some more while you make the bloody thing, go and try to find a table amidst all the wannabe writers with their cheap-ass laptops, then bus my own table AND YOU WANT A TIP? Bite me."

I would no more tip a barista than I would tip a cashier at McDonald's. It's not that I don't value them; it's that, unlike restaurant servers, they're being paid at least minimum wage.

It's almost never necessary or advisable to tip people in the educational, medical, or professional fields. So stay away from tipping teachers, life coaches, doctors, dentists, veterinarians, contractors, large business owners, and cable installers.

I mean, I thought that was obvious.

Tipping is usually done on the post-tax amount, but technically, there's nothing wrong with tipping on the pre-tax amount.

Splitting hairs here. Technically, there's nothing wrong with tipping a server 10%. If you tip on the pre-tax amount, they're going to think you're a lousy tipper. Maybe that doesn't matter. Whatever.

We all know (or we should know) to tip servers 15% to 20%, but how about those working at a buffet? Even if they aren’t serving your food, they're still bringing you beverages and clearing your dishes. Etiquette dictates you should tip about 5% to 10% of the bill.

I can't argue with that. Unlike baristas, they're actually doing services.

Tipping pizza delivery drivers can get a little confusing, says Swann, "because they’re delivering food, and we might be thinking about the 15% to 20% we tip servers in a restaurant. But that isn’t the same thing because delivery drivers make an hourly wage." A 10% tip is sufficient on food deliveries.

Yeah, no, even if they're making an hourly wage, it's a shitty hourly wage, and unlike baristas, they're using their own car, which means a lot of that wage is going to fuel, insurance, wear and tear, maintenance, inspections, whatever.

Uber gives riders a chance to tip from the app. "If you do choose to leave a tip, you can select the option that you feel that is most appropriate based on the ride that you just had," says Swann. Meanwhile, the standard tip for cab drivers is still about 10% to 15%.

Uber: I have no problem with tipping them according to how much I had to bounce around during the ride. What I dislike most about Uber is that you're expected to give each other 5 stars for, basically, not being a total dick. To me, three stars should mean "got me to destination close to estimated time, didn't get into an accident, no road rage." Five stars should be reserved for if they've hired a hooker to give me a handy in the back seat while doing all the above. One star would be only if they drove me off a cliff. But that's not how it works. Uber penalizes drivers for anything less than a perfect 5, and that's bullshit.

As for tipping them, see above re: delivery drivers.

Taxis are a bit different. These days, their credit card machine provides pre-set tip amounts. I've seen the following: "35%" "40%" "50%" as options. This is why I don't use taxis anymore.

Anyway. Off to pack for the trip. As I said, updates for the next week will be at odd times.

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