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.
I saw a Canadian goose flying backwards yesterday. I wonder if that may be a trigger for some kind of doomsday event? Nah, it's probably just a sign that the wind gusted to almost fifty miles an hour.
It seems like just about anything means the end is near.
3 of my daughters should get excellent views, clouds permitting. The one in Arkansas is just north of the upper edge of the path of Totality, but the ones in Texas and New York will have it go right over their house. Pretty cool.
Isn't that what memories are? Broken links to the past? I think many of us would be surprised if we could actually go back and see the reality of our memories.
An epic feast is held in your honor - whatโs on the table? Whoโs invited? What entertainment is provided? (Feel free to be creative with this one! COVID is not a factor and you get to choose the time period and location for your feast )
I gave a lot of thought to what to eat at such a feast, but then decided it doesn't much matter. I have a wide range of taste in food. Pizza, sushi, a formal five-course meal, steak, hamburgers, seafood, roast beef, chicken, chili, turkey... whatever. My only restriction is that I don't eat anything that's smarter than I am, so no octopus or cuttlefish.
The important thing is what alcoholic beverages will be provided. I've thought about this too, and decided: all of them.
For entertainment, someone will have to hire Bruce Springsteen. Good luck with that.
As for who's invited, all of my friends and enemies. The friends so that they can celebrate with me; the enemies so I can gloat.
In reality, of course, I'd be sitting home alone with a frozen pizza (which I'll cook first) and a six-pack of local microbrew, listening to a random selections of tunes from the internet. And that's okay, too.
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