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.

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Adherennium Plotting something

about 4 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.

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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.

August 31, 2022 at 12:04am

#1037122

Vulgar Tongue

Did you think Urban Dictionary

was something new?

The Very Proper Reason the British Library Has a Vulgar Dictionary
You can learn a lot from slang.

Like most kids, I amused myself in my youth by looking up certain words as soon as I encountered a new dictionary. Kid Me derived great enjoyment from finding Forbidden Words in school library dictionaries.

A “dictionary of the vulgar tongue” may sound like some kind of prank gift, something you pick up as a means of upping the ante on your name-calling or adding some spice to your conversations for all occasions. But you won’t find this dictionary at Spencer’s Gifts. It’s tucked away at the British Library in London, shelved and looking prim and proper in its original 1785 binding.

How much better, then, to find the 18th century proto-Urban Dictionary in such a staid institution as the British Library? It's like finding fart jokes at the Library of Congress.

[The dictionary] looks a lot like another noted 18th-century dictionary—Samuel Johnson’s Dictionary of the English Language. The only thing differentiating these two is their focus: the English language versus the “vulgar tongue.”

As the article points out, "vulgar" meant a different thing back then. Basically it was peasant-speak.

Today, “it’s one of the more important slang books ever published,” says lexicographer Jesse Sheidlower, an adjunct assistant professor at Columbia University. “Johnson made a specific effort to keep out this kind of language.”

It is not possible for me to think of Samuel Johnson's dictionary without recalling one of the funniest comedy shows of all time, of which the following is but a fragment:

Anyway...

The entries in Grose’s dictionary run the gamut from words and phrases common to laborers, military personnel, and bar frequenters to cant—the jargony language of criminals. Among the pages are such listings such as “cheeser,” another word for a fart; an “Admiral of the narrow seas,” someone who drunkenly vomits into the lap of the person sitting opposite him; and “to dance upon nothing,” meaning “to be hanged.”

One wonders how many words the dictionary contained for private parts. I once participated in an impromptu roundtable discussion where we listed every synonym for "penis" we could come up with, and while I don't remember the exact final tallywhacker, it was well into the hundreds.

But this isn’t just a collection of fun phraseology, explains Sheidlower. It’s a window into a crossroads of language at the heart of 18th-century Britain. Terms used in various underground criminal enterprises—like “bean feakers,” or bill counterfeiters—intermingle with simple words used among commonfolk like “lobkin,” which is just another word for a house or home. (Some of the words and phrases included live on into the modern vernacular with their centuries-old meaning, such as “to screw” and “to kick the bucket.”)

Whereas I'm willing to bet the vast majority of the words and phrases have been lost from common speech, having lost their relevance, or replaced by more modern equivalents. And yet, a quick glance at the contents shows that others have, indeed, persisted; some have even entered formal language. I will point out, for example, that one of the definitions of "punk" therein is "a little whore." I will also note that, since it still amuses me to do so, I looked up some of the naughtier words and was delighted to find that some of them were included—albeit with apparent self-censorship.

Grose and his dictionary gave the world a peek inside various groups in danger of having their cultures steamrolled and made the language of commoners as worthy of study as that of aristocrats.

And the article ends with a link to the digitized version of the dictionary. If you're too lazy to go to the article to find it, here it is.

.

Incidentally, there's a word in there: Frenchified. (I found it when I was looking for other words starting with F.) It means "Infected with the venereal disease." I can only assume that there exists, or at least existed, a French version of the dictionary, in which the word is "Anglified."

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