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.

September 4, 2019 at 12:58am

#965522

Lies, Damned Lies, and...

PROMPT September 4th

Did you know that WDC keeps track of everyone who views your items? To have a look at your blog’s statistics, open your blog, click the gear icon in the top right, and then click “Statistics.” You can do this for your blog or any other item in your portfolio!

In your blog entry today, share anything interesting you found while exploring your blog’s statistics. What is the profile of your average reader? Do you consider your readership when composing a blog entry? Everyone has an “ideal reader,” as Stephen King says. Who is your ideal reader?

Admittedly, I used to obsess about item stats. I quit doing that a while ago. So I went ahead and checked the current info.

Turns out my "average" reader is a rich married woman. Well, what good does that do? I want to meet rich single women. Or poor single women. Or, well, any woman who is single, really. I'm so alone.

Do I consider my readership? I suppose, in a way, though not by the demographics. Mostly I post stuff that interests me. If it interests someone else, too, great - I mean, that's the point, right? Read if you're interested; skim or ignore if you're not. I do take previous comments into account when writing blog entries, sometimes. Trying to be everything to everyone would be exhausting, and it'd never work. I'm well aware that most people (in general, as well as on this site) aren't as into math and science as I am. That's okay. Everyone has their own interests; these days, I blog mostly to practice writing. "Write every day" doesn't mean it always has to be fiction.

When I do write fiction, though, 90% of the time it's not a particular demographic I'm aiming for. No, I think that some of the greatest works of literature were not written for random people, or a particular group of people, but for one specific person. Somehow, they still end up with mass appeal. So I write for one specific person. Who that is shall remain a mystery, but you know who you are.

The other 10% of the time, I write primarily for myself.

Trying to consider reader demographics is, for me, difficult. I don't know what people want; I just know what I want to say, or at least have a general idea about it. This often doesn't mesh with what people want. I don't have the slightest idea what makes something the perenially popular "young adult" targeted story, or for that matter anything else. Nor do I know how to make my writing interesting, but I'm hoping that with continued practice and self-education, I can gain some insight into that.

I don't know if I'd still write blog entries if no one read them. I like to think that I would, but I do appreciate the conversational aspect of blogging. And for the record, I don't get angry if someone disagrees with me; I'm a grown-ass adult^{[citation needed]} and I can take it. I do get angry if I'm misunderstood - not at the person who did the misunderstanding, but at myself for not being more clear. Writers should always strive for clarity, I think; when I read something that seems deliberately obtuse or convoluted, I don't read it for long.

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