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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Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

February 19, 2023 at 10:10am

#1045084

Revisited: "No Links"

Today's trip down Memory Lane (a street which, for me, is a winding dirt road with numerous potholes) involves what was, apparently, a rare personal update from August of 2009: "No Links"

It's been pointed out to me (though I already knew it) that most of my recent blog entries have been, well, links to funny stuff. People like links to funny stuff, but maybe someone's reading this to actually find out what I'm up to.

I've since expanded my repertoire to add links to serious stuff (that I sometimes make funny), blogging contest responses, and Revisited entries like this one.

Thing is, not much has been going on in Waltzland. My wife's away for a few days, leading me to discover that bare skin sticks to my computer chair.

I want to clarify that this was what's known in comedy circles as a "joke," and is not reflective of reality. However, it was August, so I don't know; maybe I was wearing shorts. And yet, that's the part most of the comments latched on to.

Work is slow, because despite the stock market's optimism, the economy still sucks golf balls through garden hoses.

2009 was, as I recall, the beginning of a bull market that would last over a decade, finally turning bear just last year. But we couldn't have predicted that then, nor could I have predicted when the local real estate market, which kept me able to eat and drink beer, would start cranking back up. Turned out okay for me, though.

It's been raining a lot around here, which means I haven't heard shit about "drought," "water restrictions," or "hot enough for ya?" First person to mention "drought" to me this summer gets a super-soaker in the face.

As I recall, there was a local drought one summer in the 90s or noughties. The details, and the year it happened, escape me, but I do recall that after a sweltering summer with constant reminders to take shorter showers, let your lawn die, and not flush the toilet until it became absolutely necessary, and other exhortations to please, for the love of god, conserve what little water we have left in the reservoir... after all that, the local water authority complained about having lost money that year, and thus wanted to institute a massive rate increase.

This led to me swearing to never conserve water again, because the only reason to do so would be so that they could raise rates afterward.

Well, we haven't had a significant drought since, and I do try to conserve water, so, so much for that.

I've been going to a local science fiction & fantasy book club for the past few months. We meet once a month to discuss the assigned book, plus whatever other books we've been reading, and to complain about crappy science fiction movies (that is, this year, every one except Watchmen and Star Trek. Shut up, Stik.)

That was a fun club. I don't remember what other movies came out in those genres that year, and can't be arsed to look it up, so I also can't remember what I'd been arguing with Stik about. (Stik, your memory is much better than mine, so feel free to remind me.)

I think I'm the only married person there. Surprisingly enough, at the last meeting, women outnumbered men (and we didn't end up discussing Twilight).

Yes, that was a sexist comment, I know. After that, no one invited me to be a public speaker. Oh, wait, no one invited me to do that before the comment, either.

Oh, and I went to New York City over the weekend. Somehow never got around to mentioning that. I've been there three times this year, now, so it almost seems routine. Got some good pictures, though.

Three times might be my limit. Usually, I visit once or twice. During the... you know... that dropped to zero for a couple of years.

Which reminds me - I finally broke down (literally broke) and bought a Nikon digital SLR. It fucking ROCKS.

That was a good camera—for the time. Haven't used it in years. Smartphone technology quickly left its picture quality in the dust. As I have no intention of getting back into professional photography, or even serious amateuring, the built-in camera is good enough for me, and it's way easier to carry around and back up.

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