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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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December 7, 2020 at 12:01am
December 7, 2020 at 12:01am
#999783
"30-Day Blogging Challenge ON HIATUS [13+]:
7. Letter Writing Day
Write a letter to one of your favorite characters.
Which book and who's the author?

"JAFBG [XGC]:
Each year, scalpers buy the most popular holiday gifts and sell them for triple what they paid for them. How do you feel about the practice of scalping?


"Write a letter?" Oh, sure, just let me get my inkwell, ink, goosefeather quill, parchment, and blotter and arrange them all upon my writing-desk, which resideth within my conservatory. Now where did I put that sealing-wax and my signet ring?

Speaking of which, when I was a kid, I was convinced it was meant to be ceiling-wax, and I didn't understand why one would want to wax a ceiling and what that had to do with correspondence.

Also when I was a kid, I had the worst handwriting in five states. If they'd had a "worst handwriting" competition, I'd have won. We had chickens for a while, and they scratched out more legible letters than I did.

Fortunately, we had typewriters, and then computers, and I got really good at touch-typing. I still couldn't sign my name as anything but a scrawl, though. So to really address the first prompt -- and to find a way to merge the two prompts -- I have to pick a character that's able to receive email. That leaves out fantasy characters. And it probably leaves out science fiction characters because I don't think any email I send will be around long enough to get to, say, Captain Kirk. Besides, like I said, it also has to address the scalping issue, so someone who can do something about those scum would be...

Ah. I've got it.

To: batman@batcave.org
From: cathartes02@writing.com
Subject: adventure capitalists

Hello, I hope all is well with you and the Joker hasn't killed another sidekick recently.

First of all, thank you for all that you do. You are an inspiration in your dedication to justice, your code of ethics, and your impeccable fashion sense. Also, wonderful toys. Well done.

I'm writing to you this evening with a fervent request. As you know, it's the holiday season, which means more petty crime, which I realize is usually beneath your notice as you're normally off chasing Catwoman (I don't blame you) or foiling the Penguin's plans. But there's an issue which affects families all over Gotham and beyond, and I believe that you are in a unique position to do something about it.

I'm speaking, of course, about scalpers: people who buy up all the most popular holiday items and then resell them for an obscene profit. Now, at first glance, I realize this is just an extension of capitalism: get there first, invest money in hopes of a high return, charge what people are willing to pay, give your employees minimum wage or less. And I also realize you got where you are now because of capitalism (yes, I know who you are, Mr. W.). But even you have to admit that charging poor families double or triple the market price is in, at the very least, poor taste.

So, at the very least, maybe keep an eye out for these scalpers. Swoop down on top of their sleazy vans or whatever, and then when they look up, just glare at them. Maybe say "I'm Batman." That usually scares them off. Then you can do the Santa thing and redistribute the wealth to the p- oh, wait, that's communism. Don't do that. Return the products to the store and make the people buy them at retail, then.

Of course, scalping wouldn't work if people weren't willing to pay more than the retail price. You probably own some of the companies making the popular items, so this is also an opportunity for you: jack up the prices, because clearly the market can bear it, and who knows? You might make enough extra money to be able to replace Robin with a robot next time, so you won't be as broken up when the Joker does what the Joker does. Oh, and since it was my idea, I'd appreciate a commission. Say, 20% of the net?

Above all, have a batty holiday season! Oh, and if you could give me Catwoman's mobile number, that'd be great, thanks.

Regards,
Waltz


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