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:

Turkey DrumStik

about 8 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.

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

November 3, 2018 at 12:42am

#944774

Chill

There was a football game tonight.

I live close to UVA, close enough that I can hear the announcer and the music. Sometimes, even the crowd. When I do, I know two things:

1) I'm staying home; the streets are a goddamn mess.
2) Things will be crazy later.

It doesn't matter whether Virginia wins or not; people get riled up either way. Just now, sitting on my deck freezing my ass off, I heard firecrackers. At least, I hope they were firecrackers. Not much in the way of gun violence in Charlottesville; just the occasional white supremacist coming in from out of town to run us over.

I like my deck. I'll like it better when it gets replaced, if I can ever get someone to commit to giving me an estimate for the work. Right now, it's aging and weathered, but it serves its primary purpose, which is letting me sit outside while still being mere feet from a portal to the great indoors, where it's warm.

Oh, lovely. Now there are sirens. There are two times I can guarantee hearing sirens around here: just as a storm begins, and after a football game ends.

It rained here, earlier, and the air still smells of wet decay. I think, judging from the odor when the breeze shifts a certain way, that one of my cats brought me a present again, but I'm not going to root around in the dark looking for a dead mole or whatever it is.

And it's getting colder.

At least there are no bugs right now. When I sit out here in the summer, it's warm, which I prefer; but bugs crawl, fly, and hop all over the place. Few bugs appear this late in the season, but it's cold. If I'm lucky, there's one or two days in the year when I can sit outside and be warm but not plagued by arthropods.

Maybe I can get a firepit installed with the new deck. Preferably one that works off the city gas lines, because I'm lazy.

There are some advantages to being outside, I suppose. It helps me keep in tune with the seasons, for starters. While I don't much like fall or winter, they do help me appreciate spring and summer more. I live in a city, but it's a kind of suburban area of the city with actual plots of land, and my backyard is all trees and nature so I don't have to go up to the Blue Ridge to freeze my ass off.

Mostly, though, I can enjoy a cigar without stinking up the house and pissing off my housemate. I think if I didn't spark up a stogie every once in a while, I'd only be outside long enough to walk to and from my car.

Soon, it will be too cold even for that, and I'll spend all my time inside, where I belong. This outdoors shit is for the birds - and even most of them have the good sense to fly south for the winter.

7 Like • Comment • View 4 comments

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