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.

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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.

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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.

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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.

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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.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
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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.

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September 11, 2023 at 11:13am

#1055576

Hindsight

No external link today, just some personal reflections on 19 years of Writing.Com.

The problem with having an account creation anniversary today is twofold:

One, it falls close on the heels of WDC's Birthday Week celebration. On this site, that's rather like being born just after Christmas in the US: everyone's burned out on celebratory cheer, and ready to go back to being their usual grumpy selves. Or, possibly, gearing up for NaNoWriMo (shameless plug for "October Novel Prep Challenge"

[13+], which is taking signups and looking for more Contest Round judges).

And two, it coincides with another anniversary.

That other anniversary was very fresh in everyone's minds back in 2004, when I signed up here. This year, I haven't seen any mention of it at all, and I follow the news cycle pretty damn well for someone who shuns popular social media (RSS is still around, and it's easy to set up your feed the way you want it; it's just not as easy as getting it spoon-fed by the algorithms on Xitter and the like).

But it wasn't supposed to be September 11; it was supposed to be the 10th. As I recall, I had some problems getting registered way back then, and it was only about 2am on a Saturday that it finally worked. That's also the reason for the annoying 02 at the end of my username; earlier attempts to register as just cathartes failed, but locked out that option. I keep meaning to change my username, but after 19 years, it seems like that would cause more problems than it would fix.

I've told that story before, but who could read all the entries here? I sure haven't.

For the curious, I'm pretty sure this was the first thing I posted in my port: "Ghost Poem #1"

[ASR] Considering my evolution since then, it's strange that my first bit was a poem, and a serious one at that. I still do them occasionally, but I'm more tuned to comedy, these days. At least I'm not embarrassed by that poem, which is older even than my account. Not embarrassed much, anyway.

I barely remember last week, let alone 19 years ago, and I don't know a way to view one's portfolio in chronological order. So I could be wrong about that being my first item. Doesn't matter; close enough, as it was the same day I joined. That, of course, made me a Registered Author. I don't remember when I became Preferred. I also don't remember the exact date I got the blue case, but it was sometime in August of 2006... probably. Like I said, my memory sucks. I still think of myself as one of the newer moderators, when that's objectively not the case (pun intended).

And I started this blog the following New Year's Day. I took a years-long hiatus from it, but decided to keep going with the same item rather than start a new one, mostly because come on, the name is awesome.

Unfortunately, it's now almost full. Around 95% by byte size, and 82% by number of entries, not counting this one. I doubt it'll last another year at the rate I post (daily, relatively long entries), so this might be my last anniversary retrospective here. I won't delete entries, and it's unclear to me whether I'd get more space in the blog if I switched to a Premium Plus membership.

I'll design that bridge when I get to the chasm. Right now, just let me end by thanking everyone who left me anniversary notes and done Anniversary Reviews, including one of that ancient poem of mine I linked above. This is not me begging for more, only acknowledging those that have done these things. It's been a great community, and I've made a lot of friends I never would have otherwise met, both online and in person. You know who you are. While I doubt I'll be around for another 19 years, as I'm pretty sure I'm not an immortal, I'm not planning on going anywhere anytime soon. So you're stuck with me... unless, of course, you put me on ignore.

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