Complex Numbers (Book)

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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.

http://www.ddewey.net/mandelbrot/

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Write_Mikey_Write!

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A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

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a day ago
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For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

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Nov 9, 2024 at 11:04am
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Nov 8, 2024 at 12:00pm
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For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

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Turkey DrumStik

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Nov 7, 2024 at 10:19pm
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July 12, 2019 at 12:24am

#962475

The ABCs of Beer

Make an A-Z list on a topic of your choosing. Stretch your creativity! After you finish your list, write a short narrative describing why you chose the list you did and how it relates to you.

A is for Ale, the finest of yeast
B is for Beer, the best kind of feast
C is for Craft, on tap at the bar
D is for Drinking it out of a jar
E is for Ethanol, organic compound
F is for Firkin; let's all drink one down
G is for Growler that you can take home
H is for Hops, which are useless alone
I is for Isinglass, for clarity's view
J is for Juice, a citrusy brew
K is for Keg, container of ale
L is for Lager, most of them pale
M is for Malt, the grain that's so dear
N is for Ninkasi, goddess of beer
O is for Oats, a flavorful grain
P is for Prohibition, a real shame
Q is for Quaff, what you do with a stein
R is for Real Ale, a British design
S is for Sour, a popular style
T is for Tap, which I see with a smile
U is for Unfiltered, filled with a haze
V is for Volatiles, scents all ablaze
W is for Wort, which starts the beer job
X is for Xipe, the Aztec grain god
Y is for Yeast, and all of its strains
Z is for Zymurgy, the knowledge we gain

...well, did anyone really expect me to pick a subject other than beer? Still, I'm willing to bet everyone gets hung up on X and maybe Z. The trick is to start there and work backwards. Nevertheless, X is always tough unless you're willing to cheat and use something that starts with Ex.

I considered it myself because of time limitations, but then I remembered Xipe (actually Xipe Totec) who was the Aztec god of, among other things, agriculture. Hey, that counts. And I had to use Zymurgy, of course.

Beer is, of course, one of my favorite subjects. I probably could have gone with science, too, which is easier (especially because science isn't afraid to start words with X), but a guy's gotta have standards. Like forcing rhymes to make couplets work. I didn't have to do that. I hope at least some readers are amused.

Probably, I should have bolded all the first letters of each line, but come on - I have video games to play.

4 Like • Comment • View 6 comments

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