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Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
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 24, 2021 at 12:01am
December 24, 2021 at 12:01am
#1023602
Unless something unexpected happens, I believe today will be the last time I'll use my eye surgery as an excuse to slack off on blog posts.

I had the final procedure yesterday morning, and everything went smoothly enough (though not even Valium could keep me from freaking out about what was going on right in front of, and inside, my eye). But between recovering from that and wanting to do my daily French lessons tonight, both my eyes are really tired now, and the right one is, additionally, sore and unfocused. As is normal for this situation, I'm told.

Still, everything seems to be going in the right direction. I won't be able to get examined for new glasses until after the new year, but I can see enough to be able to do stuff online. Or at least I will be after another day of recuperation. Most importantly, I already have a ticket for the Spider-Man movie on Saturday, and I should be able to watch it just fine.

Meanwhile, like I said, I'm slacking off tonight to keep my eyes from getting any more tired. I expect I'll be back to my normal snarky self for my Christmas morning blog entry. Until then, for those who observe it, I hope you have a great Christmas Eve!


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