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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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Just two prompts left in "JAFBG" [XGC]. Might as well go the distance. I also intend to participate in "Journalistic Intentions" [18+] this month; if you like open-ended blog entry prompts, that should be fun.
Well, that's easy to say. Tell us about something that sounds easy but you find incredibly difficult.
Oh, there are a lot of these. Like "Just talk to her," or "Call the doctor about that."
Sometimes the hardest thing for me is just getting started, even if the task itself is easy. Like, say I've decided that today is pencil-sharpening day, the day I set aside to make sure all of my standard pencils are nice and sharp. Easy, right? Maybe a little bit boring, but ultimately satisfying to see those little curls of wood peel off the points. So it's not like I don't want to sharpen my pencils. It's just that I don't want to stop wasting time on other things.
"Okay, Me, stop looking at YouTube videos and go sharpen your pencils."
"No."
"That video ended. Let's go sharpen pencils."
"But there's another one in the recommendation queue. See?"
This was especially dangerous when I was working. The number of times I cursed myself out going, "Just. Do. The. Thing." only to have my inner voice go "Don't wanna" is embarrassing.
I don't actually have a pencil-sharpening day. As an engineer, I favor mechanical pencils. Better yet, computer solutions. The point isn't the task; the point is something that's easy it is to do while being almost impossible, psychologically, to start.
I even talked to a shrink about it once, in a session. He just shrugged. "So, you don't want to." "But I do want to." "Clearly, you don't." "Okay, clearly, I don't want to. But I want to want to." It was, I think, at that point that I acquainted myself with the concept of infinite recursion in my own brain. I want to. I want to want to. I want to want to want to. And so on to infinity, while, in the meantime, the task goes undone because I'm contemplating the vastness of the universe.
But. All of those mental blocks pale in comparison with the one phrase that is guaranteed to freeze my thoughts and actions, sending the chill of intergalactic space through my whole being, rendering me utterly incapable of action. The one phrase that strikes terror in my scarred and stony heart, because I have no idea how to implement it.
The phrase? "Be creative." |
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