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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Turkey DrumStik

about 9 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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.

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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').

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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

October 27, 2018 at 12:32am

#944263

Fear Itself

With Halloween coming up, I got to thinking today: What would truly frighten me?

Partly, this is because of a Cracked article that covers a topic I've been talking about:

http://www.cracked.com/personal-experiences-2580-6-reasons-sleep-paralysis-most-...

(Cracked used to be better. Now they mostly suck, but they do occasionally have decent articles.)

While sleep paralysis is certainly terrifying at the time it happens, I don't lie awake at night dreading it, it barely affects the rest of my life, and I wouldn't call it the scariest thing that's ever happened to me. But when thinking about what the scariest thing that's ever happened to me might be, my brain draws blanks. Possibly this is out of self-preservation - I don't want to remember something that scared the living shit out of me (note: I've never been frightened to that literal degree).

Some people are afraid of spiders or snakes. Spiders, snakes, large insects, wasps, and so on certainly startle me, but once I get over the initial WTF, they're all actually pretty cool. Not that I'd want to pet them or anything, but they're fascinating.

Or take the clown phobia thing. For some people, coulrophobia is a real thing. I like to joke about it, not as a way of facing my (nonexistent) fear of clowns, but just because it's inherently funny. I probably shouldn't joke about it because it's mean, but hey, I am what I am. I even spent a night in the infamous, haunted Clown Motel in Tonopah, Nevada

once, and the only scary part of that was that it was 17 degrees F outside and it took me an hour to figure out how to make the room heater work.

I'm not afraid of death. I've been too close to it too many times to fear it. I'm certainly not excited about the prospect, but it's inevitable, so I don't worry about it. I'm kinda terrified of dementia, though; both my parents died from it after long, slow declines and I do not want to go through that or put my friends through it (not a genetic issue; they were my adoptive parents).

And now I have to face a harsh truth: even if I did know what I was most scared of, I'd be reluctant to write it down or tell anyone about it. Not because writing would make it so; that's superstitious hogwash. But people suck, and someone would find a way to use it against me. Like if I said "there is nothing in the world I fear more than ducks," I'd get spammed with Geico ads.

(Ducks are awesome, by the way. Also inherently funny. I've said before that if you're not sure how to make something funny, just throw in a duck.)

So I guess this entry is going to end unresolved. You don't get to know my biggest fear. On the other hand, I'm not sure what it could be, either.

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