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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 19, 2021 at 12:39am
December 19, 2021 at 12:39am
#1023377
Kinda worn out right now so no major post today, or link. Just been sleeping irregularly since the surgery. I think it's knowing that I have to go through that horrific five minutes again next week.

Tonight is a full moon, but it's cloudy here so I doubt I'll get to see it. The solstice is on Tuesday (which is not something you look at, so cloud cover won't matter), and that usually manages to lift my mood, knowing that days will start getting longer. We'll see.

As for personal plans, hopefully tomorrow I'll have a movie to review, and I'm also planning to go see the Spider-Man movie on Christmas Day. My personal Christmas tradition is to drink and watch a movie in the theater. Last year, that ended up being Wonder Woman 1984, and I was nowhere near drunk enough to ignore that movie's terrible plot with its idea that humanity could act as one to achieve a common goal. I mean, read the room (yes, I know it was written before the pandemic). I trust Spider-Man will be better. Hell, it would have to be.

Like I said, short entry, but I may not be able to get one in later, so this is what you get. Until tomorrow.


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