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.

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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.

January 18, 2024 at 10:31am

#1062601

Thirties Words

I've done entries about older slang in here before. Here are some examples from nearly a century ago.

20 Delightful Slang Terms From the 1930s
These 1930s-era slang terms will blow your wig.

It's important to remember that, a century from now, if anyone's still around, they'll be doing websites or braincasts or clay tablets or interactive holograms or whatever is the tech at the time to resurrect and/or ridicule the fashion and slang of the 2020s. Yes, even "rizz." Especially "rizz."

I won't be highlighting all of them here. You can go to that link from Mental Floss. But of course, I have something to say about a few of them, starting at the very beginning.

1. Nogoodnik

Given that the suffix -nik denotes a person associated with something, nogoodnik is, expectedly, a word for someone who’s nothing but trouble.

The links provided on the page are to the OED, which is fine, but I don't think they go far enough for this complex word. See, it's essentially Yiddish. "But it's clearly from 'no good,' which is English." Sure. But Yiddish, like English, likes to borrow words from neighbors and never pay them back. Or, in this case, suffixes. "-nik" is a Slavic/Russian suffix. "Beatnik" is another English use of it, from a few decades later. One particularly Yiddish example is "nudnik," which is loosely "annoying person."

And apparently, there's a Russian word, romanized as "negodnik," which means reprobate... or no-good person. So "nogoodnik" is English-Yiddish-Russian, and we should really be using it more, but there are too many syllables in the word for it to ever make a resurgence in today's short-attention-span slang.

3. Blow One’s Wig

There's a repeated theme in jazz lyrics about "blowing one's top." Anywhere but jazz, that meant being angry, like in the cartoons when someone's face turns red and steam comes out their ears. In jazz, it seems to be about being completely surprised, but in a pleasant way. Personally, I'm pretty sure it's a euphemism for orgasm.

6. Dog’s Soup

Asking a server to bring you some dog’s soup while you browse the menu might result in a worried glance today, but back in the ’30s, a thirsty patron ordering some dog’s soup would be granted a fresh glass of water.

This one would never fly today. The sibilants would merge, leading to inevitable misunderstandings. You can order a hot dog, but not dog soup. Well, not in the US, anyway.

7. Boondoggle

The next time you’re tasked with tedious or impractical busywork, it may break a bit of tension to call it a “boondoggle.”

This word is still around, of course, but I've only ever heard it used to describe government spending of limited public value.

11. Gobsmacked

I still see this occasionally, but I think it's still mostly British.

13. Nitwittery

Nitwittery is a particularly posh-sounding word for stupidity.

I do like that word. Might have to work on bringing it back. Made me wonder about "nitwit," though, so I checked. Is it a modification of something like "nought-wit?" As in "witless?" Well, maybe

something like that. Another source thinks "nit" comes from the word for louse eggs. Which could also work, in the sense of "lousy."

19. On Sus

Another slang term 1930s people have in common with Gen-Z, sus, according to the OED, is an abbreviation of suspicion or suspect, and indicates a feeling that questionable activities are afoot.

Obviously, this one reappeared in a different form. As "sus" is only one syllable, it fits in well with emojiworld.

20. Floss

In 1938, floss or flossing was synonymous with flirting or showing off, especially about one’s possessions.

Possibly a variant of "flaunt?" Or maybe an association with more expensive stuff, as "floss" in the other sense comes from something meaning silk, which was at historically pretty high-end stuff. Hence the British use of "candy floss" for what we call "cotton candy."

Doubt this one will come back, because the meaning would be too ambiguous. "She's over there flossing." Yeah, wrong head-picture.

Several more at the link. I tend to doubt some of the etymologies, but many of the words are fun.

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