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').

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.

May 11, 2023 at 10:04am

#1049467

Divided by a Vulgar Language

I've been told that the source for today's amusing link (The Daily Mash, basically The Onion but British) is blocked in non-UK areas. Obviously, it's not blocked for me; there are ways around location-blocking. But if that's too much work, I'll understand.

'Motherf**ker' and other American swear words British people can't get away with

Obviously, the link contains swear words, and would probably be 18+ on WDC.

BRITAIN leads the world in swearing, until British people attempt to say things that Americans would call ‘cuss words’.

I was under the impression that "cuss word" is pretty much a Southern thing ("cuss" being a mangling of "curse" as "y'all" is a mangling of "you all"), but I wouldn't expect Brits to understand that nuance any more than I'd expect a Yank to know the difference between a Yorkie and Mancunian accent.

Asshole

Given that we in the UK already have the vastly superior phrase ‘arsehole’, there’s really no need to be pronouncing the word ‘ass’ at all.

On this point, I can agree. "Arse" is indeed vastly superior in most instances.

Motherf**ker

Just call him a wanker, it’ll sound better.

Here, I have to disagree. Not that it wouldn't sound better; it definitely would, no matter what your accent. But "m-f'er" and "wanker" are two different insults with two entirely different purposes, coming from two completely different takes on sexual practices. Also, the former is far more versatile, being applicable to a much wider variety of situations than merely accusing someone of incest.

Douchebag

...It never sounds right coming out of a British mouth...

Phrasing!

Also, I suspect it doesn't work in England because it's too obviously French. And "douche" is a perfectly legitimate French word that translates to "shower," as in the kind you take in the morning to get yourself clean for the day.

Darn

Even our most pathetic swearwords are infinitely superior to theirs.

Except, and I must emphasiz(s)e this to keep my US passport, for m-f'er.

Pussy

Whether used to convey the fact that you think someone is weak or a pathetic way to refer to a woman’s genitalia, British people really can’t pull this off.

Right, like "fanny" is any better. And the article specifically claims British ownership of "twat," which is obviously wrong.

There's more explanation at the link, if you can view it. If not, just remember it's because of those darn arsehole douche wankers on the other side of the pond wanting to keep their comedy to themselves.

7 Like • Comment • View 4 comments

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