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 13, 2019 at 12:30am

#966105

Favorites

PROMPT September 13th

Today, the prompt comes from Charlie ~

!

List some of your favorite books/movies and explain why you like them. After posting your entry, go comment on other bloggers' entries with suggestions based on their favorites.

This is harder than it sounds.

Life, you see, is change. Stories affect what you do and how you think; they also affect other stories, inspiring them. The new story then changes one's perception of the old story. Think of how many times you've heard something like "I like Star Wars." The inevitable response is "but the prequels sucked." But they didn't say anything about the prequels, or even the sequels - just the original movie, retroactively subtitled A New Hope. And that's not even getting into Lucas' retcons.

I ran into that myself fairly recently. For many years now, I've been saying that my favorite movie is the Director's Cut of Blade Runner. This is still true. Or at least I think it is. Is there a movie I like better? At this point, if there were, I'm so invested in "Blade Runner is the greatest movie of all time" that I would be lost if I suddenly switched. And then the sequel came out, and now it's impossible to have a dialogue with someone about Blade Runner without them bringing up the very different sequel. The sequel changed the original - without altering a single frame or line of dialogue. Or, at least, it informs our perceptions of it. Me, I prefer to pretend it never happened. Honestly, I'm not sure why I watched it in the first place. So I could have grounds for having an opinion about it, I suppose.

The reason I like that movie, incidentally, is a combination of factors: the atmospheric soundtrack, the impeccable acting, the ahead-of-their-time effects, and, most of all, the things it says about humanity. All great science fiction holds up a mirror and shows us as we are, warts and all, and Blade Runner is one of the greatest.

It's even harder for me to choose a favorite book. I read Heinlein's Stranger in a Strange Land at a very early age; it warped me, and shaped me, and for a long time I called it my "favorite." Now, I see more of its problematic nature in light of more recent social developments. Again, the book is the same as it's ever been (apart from the release of the unabridged version); it's only my perception that has changed. Don't get me wrong - considering the time it was published and what I know about the author, it's a remarkable book. But one has to read it in context, these days.

One book I read almost every year, exclusively in October, is by Roger Zelazny, who was a prolific science fiction and fantasy author of the 70s, 80s and 90s. The book is titled A Night in the Lonesome October, and the original editions (I don't know if others have been published) were punctuated by illustrations by the macabre artist Gahan Wilson. I hesitate to summarize it, because doing so can easily spoil it - I'll just say it's a horror story with a dash of humor, narrated by a very loyal dog. And in it, the author draws from various threads of supernatural literature, including Dracula, Frankenstein (the popularized version, not so much the novel), and Lovecraft.

I'm a fan of everything Zelazny wrote, but October turned out to be the last book he published before his death. Appropriate, once you know the theme. I don't know if I'd be quite so enraptured by it if he'd had the opportunity to publish more - because of the effects I've described above. Since the author died, the book remains untarnished in context.

I'm going to go ahead and list one more book. Well, a series, really. It's more contemporary than the others; the author is still working on the sequels. I speak of Brandon Sanderson's Stormlight Archives, which, look, let's face it, is way better than Game of Thrones in that most of the characters that you're rooting for don't die in painful, horrible ways. Sanderson's signature technique is to come up with fantasy magic systems that are internally consistent, as well as cultures that are alien but make sense, and these books are the pinnacle of his art... so far.

If life made sense, Stormlight would be made into a massive TV series and GoT would be relegated to the obscurity it deserves. (Yes, I read those books. Yes, Martin is an excellent writer; I just didn't like the books. No, I didn't see more than a few episodes of the series.) But life doesn't make sense, and I have to be content with the novels.

So there it is: one fantasy, one supernatural/horror, and one science fiction - just so anyone who chooses to comment as per the prompt above knows what my preferred genres are.

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