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:

Write_Mikey_Write!

about 22 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 24 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.

January 21, 2020 at 12:03am

#973843

Souvenir

PROMPT January 21st

How much of your own life or the lives of people you know do you put into your writing? Do you mine your past for inspiration, or do you create wholly new places and characters?

I mean, I write science fiction and fantasy.

Still, it's inevitable that some souvenir of my past, some moment of doubt or pain, of joy or satisfaction, whether mine or someone else's, will make its appearance in my fiction. And it should go without saying that blog entries are as honest as I can make them, within the boundaries of an imperfect memory as well as a desire to avoid identifying specific other people in less-than-ideal situations. Well... and also allowing for the occasional hyperbole or other truth-stretching for comedic effect. Never let the facts get in the way of a good joke, I say. Or a bad one. Especially a bad one.

It's inevitable, really, that the past should creep in to any writing, as that is all that is real. The future is unknown outside of a few constraining assumptions, and the present is a geometric point on the timeline, without dimension, an illusion, the limit of the recent past and the immediate future. Yes, only the past is real, but, like the grammatical tense, memory of it is imperfect - I was running somewhere, they were singing some song, she was on her way to the prom when...

The minutiae of the past are sometimes sketchy and unreliable, so I use some memory that seems sturdy as a scaffolding, a framework on which to build the specifics. Like the skeleton of a building, this defines the general shape, and while some details are clear on the blueprints, others I have to make up, or pull from other memories. Some other situations - like someone in free-fall in a spaceship - I obviously have no personal experience with, but even there I rely on memory: memory of scientific descriptions, of books, movies, and TV shows that I thought got it right (most don't).

Or if it's a fantasy world, maybe something from a dream will pop in there: terrifying monsters, shifting landscapes, rivers of metal, forests of feathery hair. Again, all part of my past, even if not a part of consensus reality.

Point is, and this goes back to what I've been saying for some time, there's nothing useless when you're a writer. You never know when something you or someone you know has witnessed, or learned, or dreamed or watched or endured, can be useful in writing, perhaps just as a metaphor or simile, much as sometimes, that spice that's been languishing on the rack might be just the thing to transform a meal from merely good to delicious.

Maybe that's why I tend to keep things around: for spice.

A picture postcard
A folded stub
A program of the play
File away your photographs
Of your holiday

And your mementos
Will turn to dust
But that's the price you pay
For every year's a souvenir
That slowly fades away
Every year's a souvenir
That slowly fades away

8 Like • Comment • View 6 comments

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