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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

March 24, 2021 at 12:01am

#1006963

What's a Wonk?

Look, sometimes I just like to trace a word's etymology.

The preoccupation of ‘wonks’

But I often get more than I bargained for. After all, no word exists by itself.

If you’re looking for evidence on how language can change, look no further than William Safire’s 1980 “On Language” column in the New York Times discussing collegiate slang—or, as Safire puts it, “campusese.”

I have a vague memory of that, but I couldn't recall the contents if you paid me.

According to that column, easy courses were called “guts,” and people who would do anything for an A were called “throats,” short for “cutthroats.” “Throats” was a replacement for “grinds,” itself a replacement for “bookworm.”

I have an alternative idea for why people who would do anything for an A were called "throats," but let's leave that alone for now. And when I went to college just a few years later, the word "gut" was absolutely still in use for easy courses. The course I took in film, for example, was officially titled "Cinema as an Art Form," which we changed to "Cinema as a Gut Form," often shortened to "Cinema-gut."

“At Yale, the grind is a ‘weenie,’ ” and “at Harvard, the excessively studious student is derided as a ‘wonk,’ which Amy Berman, Harvard ’79, fancifully suggests may be ‘know’ spelled backward. (In British slang, ‘wonky’ means ‘unsteady.’)”

As I had no contact with Ivy League people -- well, except my cousin who had gone to MIT, but we didn't speak much -- this is all news to me.

Merriam-Webster defines “wonk” as “a person preoccupied with arcane details or procedures in a specialized field” or, broadly, a “nerd.”

Meanwhile, the distinction between "nerd" and "geek" is still hazy to me. If pressed, I'd say a nerd is someone who likes to learn stuff, while a geek has more of a math/science focus. Everyone is a nerd about something, but not everyone can claim geekitude.

Webster’s New World College Dictionary, the one favored by the Associated Press, calls “wonk” slang. And though its synonyms are slightly insulting terms like “nerd,” “geek,” and “dweeb,” “wonk” is worn as a badge of honor by many people who are specialists in their field (or claim to be).

Yeah, look, "nerd" and "geek" haven't been insulting for many years now. We reclaimed them long ago. As for "dweeb," well, that's just a nerd in a bowtie.

Turns out, the word “wonk” has had many (unconnected) meanings over the years.

This is why I'm a nerd about etymology.

We are still not any closer to the etymology of “wonk.” The OED has a clue, in its entry for “wonky,” which it traces to 1919: “Of a person: shaky, groggy; unstable,” the British definition Safire cited. “Of a thing: faulty, unsound; unreliable.” The OED says its etymology is “Obscure: the German element wankel- has similar force.”

I am forced to assume that "wonk" and "wonky" have entirely different etymologies, like "candle" and "candy." Just because words sound or are spelled similarly doesn't mean they come from the same place.

The article doesn't, however, make a connection with Willy Wonka, which is a terrible oversight; seems to me that fictional character's name would have connections to both "wonk" and "wonky." You know, because he was an expert on candymaking, and more than a little eccentric.

In the end, words mean what we collectively decide they mean, and only the most passionate grammar wonk won't admit that language itself is wonky as hell.

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