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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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March 4, 2022 at 12:10pm
March 4, 2022 at 12:10pm
#1028252
Really brief entry today, because I'm playing a lot of catch-up here after coming back from my trip.

The flights back were, remarkably, both on time and not too uncomfortable, and they didn't even lose my luggage. Something is definitely off with the universe. The downside is that this gives me nothing to rant about, which makes blogging more challenging. So, what am I supposed to do, rant about having nothing to complain about? Paradox!

Tomorrow, very likely, I'll resume midnight posts of more substance, but for today, like I said, just catching up on bills and cat maintenance.

And, of course, trying to once again get used to the colder winter days here in Virginia. I don't miss the smog, but damn, the weather was nice in L.A.


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