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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Write_Mikey_Write!

about 6 hours 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

about 8 hours 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').

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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.

January 23, 2022 at 12:01am

#1025214

Catching Zs

Another tough one today from "JAFBG"

[XGC]

Tell us about something that has been difficult for you to discuss in the past, but that you're ready to talk about now.

It's not tough because of the subject matter, but because the few things that are difficult for me to talk about are still difficult to talk about. And while I've mentioned some of these things to close friends, none of them are ready for this very public forum (I have the blog set to "Allow Everyone" in the so-far-thwarted hope that offsite people will read it and want to join WDC).

I think most people, confronted by this failure of ability to directly address the prompt, would just skip it. Not me, though. Because while it's difficult to talk about certain traumatic experiences in my early life, as any regular readers can attest, I don't have a problem spewing words on damn near any other topic, whether I'm qualified to or not.

For the sake of discussions, I'm going to use language as a compression algorithm, and rename that-which-we're-not-ready-to-talk-about to the letter Z. And I don't give a shit whether you pronounce that Zee or Zed.

Since I don't want to address Z directly, I'll come at it from an oblique angle.

In a meta sort of way, this is a direct response to the prompt, because I don't think I've even acknowledged the existence of Z in here. I just kind of assumed that people would know that I had stuff I was going to keep Z-cret (yea, I couldn't help myself, but to get that pun you have to pronounce that letter as it is in the US). Because, well, doesn't everybody? Maybe you tortured animals as a kid, but didn't grow up to be a serial killer, though if you admitted to it, people would assume that you were. Maybe you're sexually attracted to ten-year-olds but never do anything about it. Maybe you stole your brother's teddy bear and tore out the stuffing because he annoyed you, then blamed it on the dog, who ended up "on a farm." Maybe you know that your parents abused you, and you're not repressing the memory, but keeping it to yourself because they weren't all bad and you don't want people to think less of them. Whatever. Everyone has a Zkeleton.

Okay, that one was a bit forced, I admit it.

Or maybe it's a secret so dark, so terrible, that you can't even tell your closest friends about it. Or your religious leader, or your therapist. Instead, you bottle it up inside, erecting a wall between it and your everyday life, and most of the time you manage to forget about it. But sometimes, usually at three in the morning when you can't sleep because you drank too much the day before and the alcohol-induced coma has worn off, leaving a hung-over wakefulness, and you hear a scratching on that wall, and you remember. But you don't dwell on it too much, because right now, that wall is one of those Japanese rice paper partitions and if you acknowledged the full and horrible truth, it would come tearing through, panting and slavering.

Sure would be nice to have some cinderblocks right now, wouldn't it? And some mortar. Or at least something stronger than booze.

It's good to know that everyone has a Z, though. At least, I assume everyone does. Wow, what if someone doesn't have a Z? I just now realiZed that this is a possibility. How well-adjusted would they be? It's hard to imagine. But I call myself a writer, so I have to try:

All the contortions, all the action movie laser-grid acrobatics you have to go through to keep anyone from finding about Z, well, you don't have to do those, do you? You don't have to spend most of your waking hours desperately trying to forget it, and the rest carefully ensuring that no one finds out about it.

On the other hand... in that imaginary, utopian situation... where's your mystery? You have nothing to hold back, so those few people who give enough of a shit about you to get to know you, well, eventually, they just... know you. And then you're boring.

So yeah, maybe I'll hold on to all of my Zs for the foreZeeable future. I just hope I die before I get AlZheimer's and end up Zpilling the beans anyway -- the one bright spot being that no one would believe me if I'm Zpewing Ztuff if I've got dementia. I'm something of a fiction writer, after all, and maybe it was all part of some plot or another that never got written.

Or maybe it did, and I've passed off unbearable fact as fiction.

You'll never know.

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