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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June 20, 2022 at 12:05am

#1034016

Lousy Lurks

Another entry for "Journalistic Intentions"

[18+]

Breaking In to Talk

You know, the whole thing about tropes is that while they can be clichés, they aren't usually; they're just storytelling elements. What makes a cliché is something that's overused to the point of losing its impact, which is a very subjective thing. So the whole "person comes home and discovers their antagonist sitting in an armchair brandishing a pistol" thing can still work, even though it gets used a lot, especially if you do something new with it. The Blacklist, for example, does this to great effect -- with the twist that it's almost always the antihero protagonist of the series doing the lurking.

What doesn't work, what has never worked (in my not-so-humble opinion), one version of this trope that doesn't get mentioned on the page, is the jump scare when someone gets in their car and the bad guy suddenly appears from the back seat.

While I don't currently own a car (long story, and I've already covered it here), I guarantee you that if I did and if someone were lurking in the back seat, I'd notice them before I even got into the car. Even assuming I've decluttered it recently (not a safe assumption, by the way), it's literally impossible for me to miss the bulky shape of a human as I'm walking up to the thing, keys in hand. It doesn't matter how dark it is; it's never so dark that you can't at least see the silhouette of a fellow homo sapiens in the back seat. If it ever is that dark, you wouldn't be able to see the goddamned car to open the door. And even if they're lying in the floor well, you'd still see something's off, especially as once you open the door, the frickin light comes on.

If you can't see your enemy sitting in the goddamned back seat, you shouldn't be driving anyway, because your vision sucks.

I can excuse this version of the trope if the vehicle involved is a van or RV, or something else large and with lots of room to hide. Or if the person lurking has some sort of invisibility or shapechanging superpower, in which case, come on, there are other ways for them to jump out at you. Otherwise, you just can't hide a human in the back seat of a car, Border Patrol insistence notwithstanding.

Maybe I've just been conditioned from years of watching movies and shows with the back-seat-hiding jump scare person, so it's become second nature to me to glance into the back seat to ensure no one's lurking there. But every time I see it on a show, whether it's set at night or in the brightest sunshine, it breaks any suspension of disbelief I might have had.

So if you're going to do that, make me believe it. Maybe it's a little person. Maybe they were hiding in the trunk and came in through the rear seats while your attention was on the road. Maybe they do have one of those superpowers.

And if you're doing the standard version where someone comes home to find the bad guy sitting in their favorite armchair in the dark, at least don't telegraph it with scary music.

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