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!

about 2 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 3 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').

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.

November 12, 2023 at 9:43am

#1059365

Revisited: "Real Men Don't Worry About..."

Another Sunday, another exhumation from the archives... though this one isn't buried that deeply; it's from early March of last year, featuring an article from six months prior: "Real Men Don't Worry About What a Real Man Is"

The link is from Cracked, so it's still around

as of today. I can't speak for how timely it still is; if you do the math above, you'll note that the article was from over two years ago, and things were... well, they were a little different in 2021. I don't follow trends closely enough to know if there's still a burgeoning "reclaim your manliness" industry, for instance.

As I've noted, one of the reasons I do these, apart from my blog rapidly running out of space and I'm trying to start to bring some sense of closure to it, is to see how my perspective or opinions might have changed in the intervening year or years (anything from before 12 months ago is fair game for these randomly-selected entries). But having re-read the entry, and the article, I'm not finding any notable evolution in my ideas on the subject.

I will highlight a few things, though:

Me: ...my body wash, which is also a shampoo, conditioner, salad dressing, cake icing, and engine lube.

I was quite proud of this line, and even received a positive comment about it. Hopefully, it's clear that it was a joke, but the reality is that my hair product is a) marketed to men and b) a "3-in-1 shampoo, conditioner, and body wash." Recently, it occurred to me that the cultural assumption still holds in the US that men have short hair, and that, more than sociological or biological factors, or even marketing, may be behind the labeling—though I imagine that it's attractive to many heterosexual men to have just one all-encompassing product to use, if only because their partners have taken up all the room in the shower caddy with their own various products.

Though I don't have that problem, I still appreciate its versatility and simplicity. Problem is, though, I haven't gotten a haircut since before the pandemic, and my mane was already fairly well-developed when all the barbershops and hairdressers temporarily shut down. At this point, it's pretty much full-on The Dude. While I'm glad I still have most of it at my age, I wondered (you know, one of those epiphanies you sometimes get in the shower) if I shouldn't look for something more designed for 80s-rock-star hair. But, you know, being men, long-haired hippie freaks and rock stars don't generally talk openly about hair care.

So here I am, talking openly about hair care. Because, as you might guess from the earlier entry's title, I don't worry about what a "real man" is.

Whatever; I'll keep using my all-in-one until it no longer works for me.

Another comment wondered why I didn't expand more on the final point made in the original article. I can't speak for my attitude at the time, any more than I can remember what I had for lunch that day, but upon re-reading that part of the article, I find I simply don't have much to add. I don't know what goes on in other men's heads any more than I know what my cat is thinking. The header includes the phrase: "Men Are Now Lonely, Isolated, And Scared"

Even if I agree, which I'm inclined to do, I don't have answers. Personally, I'm not lonely, even when I'm alone; I don't feel isolated, because I have friends; and apart from the occasional jump-shock from an unexpected indoor spider (they get relocated outdoors) or when I had to face eye surgery (which I came out of just fine), I don't live my life in fear.

If there's anything I could work up a comment on, it's this bit from the article:

If we insist on idealizing the '50s, maybe we should focus on the part where masculinity meant contributing to your community. That’s the real difference between men today and back then.

Guessing here that by "your community" they mean your physical location. Most of us have communities online, and they could be comprised of people from all over the world. For a time, as an example, I was gaming with a group that included someone remoting in from India, which is almost as far away as it's possible to get and still be on the same planet. And then there's this site, of course.

But in terms of local community, I don't have much of a presence. Yesterday, I made a brief and rare foray into the wild in order to attend a book discussion and signing by three of my favorite authors, all of whom live nearby—but I would never have known about their work if I hadn't found them online first.

Many years ago, I participated in a fantasy & science fiction book club, in person. Perhaps I need to find one of those again. Maybe find some decent shampoo, first.

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