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 8 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.

1 Like

Adherennium Plotting something

about 10 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.

January 24, 2024 at 12:40pm

#1062909

Pronouncements

As I'm someone who gets information more from reading than from listening, sometimes I'm prone to pronunciation errors. I'm okay with this; I consider them more literate than spelling errors. So, from Lifehacker, some actual decent information:

How to Actually Pronounce 'Worcestershire,' 'Açaí,' and Other Commonly Mispronounced Words

My worst was "quinoa." How the ever-living fuck was I supposed to know it didn't rhyme with Genoa? So much for "never eat anything with ingredients you can't pronounce." (Which is a dumb rule anyway that only encourages ignorance.)

I’m no prescriptivist—words are yours to do with as you will, so pronounce ‘em however you like.

The obvious problem with this philosophy, when taken to its logical endpoint, is everything ends up being pronounced "Bob." Bob, bob bob bob Bob bob bob; bob bob bob bob.

Gyro

I saved this article because of this word alone.

“Gyro” is either a shortened form of “gyroscope” or the name of a Greek lamb sandwich.

It's not a sandwich. It's a taco.

In the unlikely event that you’re talking about gyroscopes enough to need to shorten the word, it’s pronounced “jeye-roh.” The greek sandwich, according to Websters, is called a “yee-roh” or a “zhir-roh.” It’s rhymes with “hero.”

I'm going to mock that site for misusing "It's" in a completely new improper way. Which, by Waltz's Second Law of the Internet, means I've probably got an error in my own writing here somewhere.

As an aside, those things that are maybe-sandwiches that most of the US calls a "sub" or maybe a "grinder?" In New York, the traditional name for them was "hero." For years, I assumed (shut up) that this was an Anglicization of "gyro" (the food that is not actually a sandwich). Because, you know, both involve filling bread with stuff. That turns out to probably not

be the case. The etymology of "hero" for the food isn't really clear, though.

Interestingly, the Greek word for “to turn” is the root of the word for both the sandwich and the machine, but the terms came into the language at different times, so we don’t say them the say way.

I can't confirm or deny that, but I was able to determine that it doesn't have to be made with lamb meat.

Açaí

The berries from the Açaí palm tree that grows in South America have become popular enough that you may be called upon to say their name at brunch. If so, it’s pronounced aa-saa-ee.

Fair enough. Another one I'd only seen printed, never pronounced.

Nguyen

“Nguyen” is a common last name in Vietnam, and Vietnamese is a little tricky for English speakers.

To call it a common last name in Vietnam is to master the art of the understatement. About a third

of the population has that name.

I met a blackjack dealer in Vegas once whose name was Tu Nguyen. I was just drunk enough to assert that, well, that's what I'm here for: to win. She was too sober to appreciate it. No, actually, probably every drunk cracker who's ever visited Vegas made the same "joke." Sorry, Tu. I promise I'm never a mean drunk, but I am a stupid one sometimes.

Oh, and it's important to remember that "Nguyen" is a transliteration from a pictographic language. Why they couldn't create a more approachable spelling is beyond me.

Gif

I don't care what the article or the format's inventor says. It's a hard g. I have spoken. Hell, I wouldn't change my mind if the clouds parted and Jod themself pronounced [pun intended] that it was "jif." (It's graphic interchange format, not giraffe interchange format.)

Worcestershire

Worcestershire is a county in England where they invented a delicious condiment in the 1830s.

And that word was Kid Me's introduction to how England can't pronounce English.

Phở

This Vietnamese noodle soup is pronounced “fuuh,” according to Websters, but “foe” seems to be catching on fast, at least if you’re an English speaker.

Thus leading to my second favorite restaurant name of all time: Phở King. It's phở king glorious. If you get sick there, well, phở cough. Want it to go? Phở cup.

My favorite restaurant name of all time? Same cuisine: Viet Noms. There are probably dozens of them by now, but the first one I saw was in central California. (Great food, incidentally.)

There are more in the article, all English... but many derived from French, so it's no wonder we phở kit up.

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