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!

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').

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.

July 26, 2019 at 12:09am

#963196

Inspiration

I need your help to fill the Challenge War Chest with new prompts. Write four blogging prompts and choose one of your own to write your entry on.

1. What do you do when you are out of inspiration or ideas?

2. Gojira (aka Godzilla) invites you over for tea. What do you bring as a gift?

3. Visualize world peace.

4. What is your favorite storytelling medium, and why? Face-to-face? Movies? Novels? Audiobooks, audioplays? Stage productions? Comics? TV shows? Tweetstorms? Concept albums? Something else?

For my own entry today, I'm going to talk about number 1 - mainly because I was out of inspiration and ideas, so I blatantly stole the other three prompts from my friend (with her permission of course, so I guess it wasn't actually blatant or stealing).

I know, I know, you were hoping I'd talk about Godzilla's tea party, but my mind is still drawing blanks on that one. I mean, what do you get a kaiju who has everything?

First of all, while some of us have the luxury of simply not writing when we don't have the inspiration, most serious writers have a schedule and deadlines to meet. Many authors recommend daily writing, regardless. As far as I'm concerned, blogging counts. But whatever your writing goals, you're probably going to come up against a brick wall occasionally.

Personally, I think inspiration is overrated; it's not necessary for getting work done. And getting ideas is more a matter of perspective than anything else. Maybe you see your cat over there licking her asshole. You can ignore it, you can accept it as a cat being a cat, or you can find a way to write an entire essay about ass-licking. Or a story where you get a chance to ask the cat what the deal is with that. And what's this purring thing all about, anyway? Be warned, though; you might not like the answers. If she deigns to answer in the first place.

Point is, ideas are everywhere if you look for them. It's just that today, I chose to look for them in a friend's mind instead of my own.

Another technique that I've used with some success - and here I'm not talking about success as in "writing excellent fiction" but "at least getting inspiration for shitty fiction" - is to do what I call a Core Dump because I'm a UNIX geek from 'way back.

I know I've written about this before, but for those of you with the presence of mind to avoid reading through old entries, it's been recommended by actual writers, too. They call it different things, like "freewrite." I'm pretty sure I came up with the idea independently, but it's not like I have any influence, so if someone else wants to take credit for it, fine.

The idea is to start with a blank page - either paper or virtual, whatever works for you - and just start writing down your thoughts as they come. No one else will ever see this, ideally, and the purpose is not to come up with good writing, but to focus your mind and get into writing mode - so absolutely do not edit this. It tends to get rid of surface thoughts so you can get to your core (hence my name for it). I don't know about anyone else, but I find myself thinking in circles a lot, but writing helps to break out of that bind.

Some ideas might come out of it, but that's not the main reason. The main reason is to just do it, to steal a slogan from an ethically questionable corporation.

Even if you do see a good idea emerging, just get it down and forget about it. You can go back and find it later, after which you can destroy the evidence.

When I do this, I shoot for at least one page, written or typed, but generally once you've gotten that far, you have the momentum going. There's no limit to this, but it's not meant to be yet another means of procrastination, so maybe set a timer or something. If you later find the time is too short or too long, you can always adjust it for next time.

The other suggestion I have while doing this is: don't force your thoughts; just let them come, like they do when you're daydreaming or whatever. I know, I'm treading dangerously close to the "mindfulness" bullshit that's making the rounds these days, but this is really not the same thing. It's not a spiritual or psychological practice; it's simply a practical method for clearing your head to focus on the writing you're supposed to be doing.

That said, if you have other ideas for this, by all means, don't wait for the prompt to come around in rotation (if it does); share them with me in the comments. I can always use ideas.

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