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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Write_Mikey_Write!

a day 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

a day 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').

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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

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

September 27, 2019 at 12:25am

#966853

Quote

PROMPT September 27th

Today, the prompt comes from Prosperous Snow celebrating

!

Share a quote from either your favorite author or your favorite book and discuss why you like it.

Anything contemplated for too long, or repeated often enough, loses its impact. So it is with favorite authors, books, and quotes: I've had several over the years, and their meaning has shifted for me.

That's how we get clichés, you know. Every cliché is born as profound poetry. A knife starts life with a gleaming, razor edge; use and familiarity dulls it, inevitably. Knives can be honed, of course; a cliché, once blunted, can never regain their sharpness. But sometimes, if you try, you can remember the feeling it left you with the first time you heard it.

Ask me tomorrow, and I'd probably pick a different quote, a different author. If you'd asked me yesterday, I'd have probably picked a different quote by a different author.

But the night is deep, there's a portentous chill in the air, and October looms, so today's quote comes from Roger Zelazny's A Night in the Lonesome October, a book I mentioned in here some time ago. Days? Weeks? Time morphs.

Such times are rare, such times are fleeting, but always bright when caught, measured, hung, and later regarded in times of adversity, there in the kinder halls of memory, against the flapping of the flames.

Read it slowly. Read it out loud, if you can. Feel the rhythms and the way the words trip over themselves. Contemplate the feelings it evokes.

I'm not even sure I can explain why I like it, which is a shitty position for a writer to be in. But it's not just a struggle to find the right words; it's also something related to what I said about clichés, above: regarding anything too closely, trying to explain it to oneself, well, that turns it into something lesser, and I don't want to do that with this quote.

One of the most absurd plagues ever inflicted upon the literary world is deconstructionism. No, some things should be left as they are, and I think this quote is one of them.

It's even better in the context of the scene it's in, but I don't think the particulars matter. I can apply it to any moment of joy or delight, make it something to help me get through the inevitable darkness.

That's one reason I'm so adamantly opposed to the "live in the moment" philosophy. Sure, sometimes it's nice to forget the bad things that happened in the past, but is that any reason to ignore the good ones? No. No, it is not.

In fact, Zelazny had a quote about that, too: "It is anticipation and recollection that fill the heart—never the sensation of the moment."

And now I've gone way beyond what I intended to say.

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