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 13 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 15 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.

April 14, 2022 at 12:01am

#1030689

How To Write

I finally managed to set up my new computer today. Fortunately, my bookmarks seem to have transferred with no problem. Thus, I continue to talk about articles I've found online.

This one is about writing.

What’s Needed is Magic: Writing Advice from Haruki Murakami
Also: talent, focus, and endurance.

I'm betting those last three are way more important. And possible.

If you can believe it, Japanese novelist, talking cat enthusiast, and weird ear chronicler Haruki Murakami is over 70 years old.

Not to sound provincial or anything, but... who?

Apparently he does write in genres I read, but I've still never encountered his work.

To celebrate him, and as a gift to those of you who hope to be the kind of writer Murakami is when you are in your 70s, I’ve collected some of his best writing advice below.

I highly doubt I'll make it that far. But I'll read the advice anyway.

“I think the first task for the aspiring novelist is to read tons of novels. Sorry to start with such a commonplace observation, but no training is more crucial. To write a novel, you must first understand at a physical level how one is put together . . . It is especially important to plow through as many novels as you can while you are still young. Everything you can get your hands on—great novels, not-so-great novels, crappy novels, it doesn’t matter (at all!) as long as you keep reading..."

Okay. Check. I read a lot more when I was young than I do now, and what I did read, and continue to read, include badly written books. After all, a negative example is still an example.

“It’s true. There aren’t any new words. Our job is to give new meanings and special overtones to absolutely ordinary words.”

Well. We get new words all the time. I'm especially fond of "yeet." But still, context can give words new strength and meaning.

Explain yourself clearly.

I'm often amazed at how many writers think this is bullshit advice. They usually write in the "literary" genre, where obfuscation and incomprehensibility are often mistaken for depth.

Share your dreams.

Look, do you want people to read my stuff, or run away screaming in terror? Stephen King would look at my dreams and go, "goddamn, that's fucked up."

I can only assume he means, here, the other kind of dreams, not the sleeping ones.

“I myself, as I’m writing, don’t know who did it. The readers and I are on the same ground. When I start to write a story, I don’t know the conclusion at all and I don’t know what’s going to happen next. If there is a murder case as the first thing, I don’t know who the killer is. I write the book because I would like to find out. If I know who the killer is, there’s no purpose to writing the story.”

That's... okay, great, that works for him. Just don't put a butler in it, I guess.

Hoard stuff to put in your novel.

Yeah, I think he means ideas here, but I have plenty of physical stuff hoarded, too.

Anyone know what to do with an obsolete computer or five?

“When I’m in writing mode for a novel, I get up at four a.m. and work for five to six hours. In the afternoon, I run for ten kilometers or swim for fifteen hundred meters (or do both), then I read a bit and listen to some music. I go to bed at nine p.m. I keep to this routine every day without variation..."

And we're done here.

Okay, not really, but again: four a.m. is sleepy time, not wakey time.

“After focus, the next most important thing for a novelist is, hands down, endurance..."

I'd say this is probably true for any work, not just the creative kind.

Write on the side of the egg.

...you'd have to go to the link to try to make sense of this one. I still can't.

“In every interview I’m asked what’s the most important quality a novelist has to have. It’s pretty obvious: talent. No matter how much enthusiasm and effort you put into writing, if you totally lack literary talent you can forget about being a novelist. This is more of a prerequisite than a necessary quality. If you don’t have any fuel, even the best car won’t run.”

Welp, I'm boned.

. . . unless you work really hard!

Yep. Double boned.

Anyway, I thought it was worth sharing, even if you've never heard of this particular writer. I like seeing how others view the work.

5 Like • Comment • View 4 comments

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