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 22, 2019 at 12:23am

#966577

Dated Material

PROMPT September 22nd

Today, your prompt is from bobturn!

What was the first thing you remember writing that made you want to be a writer (casually or professionally)?

I have a vague memory of writing some sort of story in fifth grade, and getting praise from the teacher for it. I have no idea what I actually wrote. Really, I have no idea if it was actually any good, or if she was just one of those teachers who knew how to encourage her students.

In any event, I think that's what led me to believe that I may actually be able to string words together in a way that people might appreciate. Thanks, Miss Chester!

Fortunately, whatever I wrote back then (likely in cuneiform on clay tablets) did not survive the ravages of time. I'm certain it would embarrass the living fuck out of me if someone discovered it.

I'd read somewhere that it's a good idea for a writer to keep a journal, so I did that, too. Several handwritten notebooks' worth of 'em. I even called them "diaries." I had some idea that it wasn't a terribly masculine thing to do, but my parents were ahead of the curve in not trying to shame me by enforcing strict gender roles.

Thank everything in the universe those writings are lost, as well. I don't envy today's kids and the permanent record of their juvenile maundering.

The earliest thing that I wrote that survives - at least that I know of - is a poem I ventured when I was, I suppose, seventeen. Hell, I even put it up here: "Bench Fry"

[13+]. Even the appearance of that poem on this site is fifteen years old, now. The Author's Note is way outdated; for starters, this was before the introduction of dropnotes to this site, so I'd collected a bunch of notes in a book item and linked individual entries.. I keep thinking I should update those older items with some of those newfangled dropnotes, but I have issues when it comes to changing stuff that's been a part of my persona for so long.

Before you scoff, yes, I'm aware that the poem sucks. But I wanted to keep something from back then.

Anyway, despite a couple of attempts, I still haven't been published. Partly that's because I haven't tried very hard. Also partly, that's because I'm still sure my stuff isn't good enough. Maybe it never will be. But I gotta write anyway.

On a personal note, if you've been following along, you might have gotten used to me posting shortly after midnight every day. I'm going to a conference for the next few days, and while I'm pretty sure I'll have opportunity to write in this blog to these prompts, the timing might be different on Monday, Tuesday and Wednesday. Likely you don't care, but the answer to "Hey, where's Waltz?" will be "Washington, DC. Drinking."

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