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 an hour 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').

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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.

May 22, 2023 at 8:15am

#1049962

Thumbs Out

Just an easy article today, and writing-related:

Please don’t let anyone Americanise it!

Clearly, they didn't Americanize the headline.

Born in Cambridge in 1952, Douglas Adams was best known for creating The Hitchhiker’s Guide to the Galaxy, a wildly successful project that began in 1978 as a science-fiction comedy radio series and eventually evolved to become something much larger, in many formats and in many languages, adored by many millions of people around the world.

I'll just point out that he did a lot more than that, including writing for Doctor Who, but it's Hitchhiker's that has embedded itself into public consciousness. Well, maybe not "public," but at least in the circles I frequent, one sign of certain intelligence is a good Hitchhiker's quote. Or a bad one.

This typically entertaining letter, which was actually a fax, was sent in 1992 to US editor Byron Preiss, whose company at the time was producing a comic book adaptation of Adams’ ever-expanding opus. Having noticed some unnecessary changes, Adams was keen to give some feedback.

I wish they wouldn't do that. Sure, Hitchhiker's has been translated into dozens of languages, but I find it offensive when they translate from British to American, as if we're too dumb over here to recogni[z/s]e that Brits spell a few words differently and have different words for several things than we do. I grew up reading both American and British literature, and while the differences did confuse me for a while, in the end, I feel like I became a better reader and writer for it.

Probably the worst offense was when they translated Philosopher's Stone to Sorcerer's Stone in the Potter books.

Anyway, the rest of the article is the letter itself, which is written, not unexpectedly, with hints of his signature dry humo(u)r. I'll just quote a few passages here.

A thing I have had said to me over and over again whenever I’ve done public appearances and readings and so on in the States is this: Please don’t let anyone Americanise it! We like it the way it is!

So it's not just me. Making it American would be like trying to do an American version of Black Adder, with American actors who have American accents. I know they did that sort of thing with a series (The Office, maybe?) but I never saw either version.

Though Hugh Laurie (who was in Black Adder), at least, does a great American accent.

The ‘Horse and Groom’ pub that Arthur and Ford go to is an English pub, the ‘pounds’ they pay with are English (but make it twenty pounds rather than five – inflation). So why suddenly ‘Newark’ instead of ‘Rickmansworth’? And ‘Bloomingdales’ instead of ‘Marks & Spencer’? The fact that Rickmansworth is not within the continental United States doesn’t mean that it doesn’t exist! American audiences do not need to feel disturbed by the notion that places do exist outside the US or that people might suddenly refer to them in works of fiction.

It is simply not possible to get the same effect if you substitute a British pub with an American bar. While there are a few drinking establishments in the US that approximate the British pub experience, the culture is still completely different.

Of course, this is only a problem for the very beginning of the story, when Earth still exists. (Spoiler)

Or we could even take the appalling risk of just recklessly mentioning things that people won’t have heard of and see if they survive the experience. They probably will – when people are born they haven’t heard or anything or anywhere, but seem to get through the first years of their lives without ill-effects.

Those sentences are pure Adams.

(Incidentally, I noticed a few years ago, when we still had £1 notes, that the Queen looked very severe on £1 notes, less severe on five pound notes, and so on, all the way up to £50 notes. If you had a £50 the queen smiled at you very broadly).

Quoting this because it legitimately made me laugh. Damn, I miss Douglas Adams. Neil Gaiman is the closest we have to him now, and while one of my favorite writers, he just can't do comedy.

One other thing. I’d rather have characters say ‘What do you mean?’ than ‘Whadd’ya mean?’ which I would never, ever write myself, even if you held me down on a table and threatened me with hot skewers.

I suspect the latter construction is a feeble attempt to render a British accent in dialogue. No. Make the thing British enough, and our minds will provide the accents.

I rarely close one of these entries with a direct quote, but it seems appropriate in this instance:

Otherwise it looks pretty good.

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