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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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December 13, 2024 at 6:26am
December 13, 2024 at 6:26am
#1081102
1827.

No, I'm not referring to the year. 1827 is what you get when you multiply 365 by 5, and then add 2.

Yes, today is not only Friday the 13th, but it's also the day I claim a five-year daily blogging streak, having shat an entry out every single day between December 14, 2019, and today: one thousand eight hundred twenty-seven entries. (There were two leap days in there, hence the "add 2.")

Granted, they weren't all great entries. Some of them were probably not even very good. But I put thought and effort into each of them, and I really did do one every day (as defined by WDC time, midnight to midnight); we're not set up here to release entries at some scripted time, or to make up for lost days.

But that's the limit. There will be no six-year blogging streak, at least not in this item. With fewer than 100 entries left in its capacity, the end looms like a kaiju over Tokyo. I thought about ending it today, but nah. Or maybe on the solstice, because that would be appropriate. Or on December 31, because the very first entry was on a January 1. No, I think I'll make the attempt to continue until entry #3000, and then... hell, I don't know. Take a break? Start a new one? Retire from writing? I haven't decided yet, and, knowing me, won't decide until the very last possible minute.

Well, I promised something different today, and there it is: a great big brag. Tomorrow, I'll be back to my usual humble self. Hey... stop laughing.


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