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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Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 15 hours ago
In response to "Extro Special"

I'll also use the spelling extrovert because if I use extravert my spell checker flags it. In college psychology our professor termed his own words, innervert and outervert because he thought they fit better. I, however, thought they sounded like definitions of belly buttons.

1 Like

Kåre เลียม Enga

about 21 hours ago
In response to "Extro Special"

I probably fit omnivert best. I'm temperamental.

Words change... definitions change... we change.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Sensational"

They say carrots can improve your eye sight, but it's been proven that drinking alcoholic beverages can make you see double.

After stating this, I find myself wondering why hasn't anyone tried fermenting and distilling carrots and marketing it as a vision tonic?

2 Like

🌖 HuntersMoon

a day ago
In response to "Sensational"

OK, look around you and observe (where possible) the reality of the newly revealed "facts." It's pretty clear that "Smartphones make you a hell of a lot of folks stupid."

2 Like

Elisa: Snowman Stik

a day ago
In response to "Sensational"

Thank you for reminding me to check on Retraction Watch.

https://retractionwatch.com/

3 Like

tj-Merry Mischief Maker

Dec 26, 2024 at 4:20pm
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

Dec 26, 2024 at 1:07pm
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

🌖 HuntersMoon

Dec 26, 2024 at 10:00am
In response to "Gray Matters"

I've always believed "better gray than gone away..."

2 Like

tj-Merry Mischief Maker

Dec 25, 2024 at 3:02pm
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

Dec 24, 2024 at 5:16pm
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

February 13, 2024 at 9:33am

#1064118

Lurk in the Woods

My (usually very reliable and speedy) internet's been out since last night. Apparently a tree fell on a power line, and they have to wait for the power company to clear it, and then do whatever arcane ritual spell necessary to restore the servers or whatever. The only thing saving me from losing my mind is that I have a backup connection. Always have backups for critical systems. Consequently, I'm able to post this (somewhat relevant) entry for "Journalistic Intentions"

[18+]:

Lurk in the Woods

I call it somewhat relevant because that link is to a photo and, as the title suggests, there are trees. There's also a deer.

I have trees. My house backs up on a ravine. The ravine meanders down to a stream. The stream flows through woods, and the woods extend all the way up the ravine, on several private lots, ending with my own. Sure, I live in a town, but not far from the edge of it.

Much as I like to rag on the outdoors, I like having trees in my backyard. Well, apart from the occasional anxiety attack whenever it gets windy around here, anyway. Sometimes, deer wander up the ravine and, on rare occasions, they'll snoop around my yard. Now, you might think I have a hate on for deer ever since one of them totaled a car that I quite liked, stranding me in the middle of South fucking Dakota, but I don't blame the deer population here for that. Besides, I felt sorry for the one who hit me; that must have hurt. So, no, I enjoy seeing the deer when they come around. I've never been able to get a good picture of any of them, as they spook at the slightest sound or movement, but they've been here in groups or alone. The guy across the street from me was a hunter, so I can only imagine them driving him crazy.

But what I'm sure is even more maddening for him is that, for a while, one of those deer was white.

Now, white deer

are rare, but not that rare. They do tend to stand out, though, especially at night, glowing like a unicorn while their deer brothers and sisters are partially camouflaged. I wouldn't be surprised if spotting white deer at the limits of firelight contributed to the unicorn legends, but I have no proof of that happening.

Nor do they have mystical powers.

And yet, being visited by the white deer on several occasions, I felt lucky. I'm not saying she brought luck, just that I was lucky to see her.

But that's not the weirdest part. Lucky enough to glimpse a white deer, but, one night, out on my deck, I caught a white streak out of the corner of my eye. I turned to look... and beheld not the one white deer, but two of them, accompanied by a bevy of ordinary-colored ungulates.

And, naturally, they ghosted off into the woods before I could get a photo. I guess that encounter was meant for me alone. These days, the only way people accept something happened is to have a photograph of it, so it wouldn't surprise me if people don't believe me.

That's okay. I know I saw them, and they saw me.

7 Like • Comment • View 4 comments

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