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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 12, 2021 at 12:08am
December 12, 2021 at 12:08am
#1023096
Little bit different format today; I'm not up for dealing with a link right now. Yesterday, an old friend stopped by, with her husband, and we all took advantage of the 60s (Freedom Units) outdoor temperatures in December by hanging out on the deck and getting completely plastered.

Good to do that sometimes.

Instead, I wanted to note that today is December 12, which means that if I make a blog entry tomorrow, the 13th, then I will have written an entry in here every day for two calendar years. I didn't really set out to make this accomplishment, but once I realized I was doing it, I figured, why not keep it up?

With eye surgery coming up fast (eek), I'm not sure if I'll be able to extend the streak. But I'm going to try. Just don't expect the regular schedule for the next couple of weeks. I may post late, if at all.

Still, the real satisfaction, for me, comes not from slavishly sticking to the daily writing exercise, but from the interaction I have with readers. I appreciate all the comments. So to mark two full years of blogging every day, let's have a...

*StarB* *StarB* *StarB*


Merit Badge Mini-Contest!


As this is, after all, my personal soapbox, I get to use it to celebrate some of my few accomplishments in life, such as the aforementioned two years of blogging every day. But I also want to hear about yours. So in the comments on this entry, tell us about one of your recent accomplishments -- or one that you hope to achieve soon; either way.

Notes:

*Donut* I will award at least one Merit Badge if there are any comments today.
*Donut* I may award more than one at my discretion because I'm feeling generous.
*Donut* Since I just sent a metric asston of Merit Badges to people who completed October's NaNo Prep, CR is not guaranteed.
*Donut* Merit Badge(s) will go out tomorrow, December 13, so you'll need to comment here by midnight tonight, Sunday 12/12/21, to be considered. But if you happen to see this entry later, your comment is still welcome.


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