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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 10 hours ago
In response to "Global Domination"

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.

1 Like

Adherennium Plotting something

about 12 hours ago
In response to "Global Domination"

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

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

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.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

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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