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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Write_Mikey_Write!

about 6 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 8 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 23, 2021 at 12:03am

#1010590

By Any Other Name

PROMPT May 23rd

Write about nicknames. What nicknames do you have for people in your life? What nicknames do others use to refer to you? Do any of these names have an interesting story for how they came to be?

I'm not real big on nicknames. I mean, if someone's named Edward and wants to be called Ed, then I call him Ed. If someone's named Zachariah and wants be called Wormy, okay, fine, I'll call him Wormy.

I've usually resisted the temptation to come up with my own nicknames for people, because I never know how they'll take it. There have been exceptions. One of my best friends started out here with the username dogfreek. She was young at the time, so I called her Puppy. That one stuck. Somehow, we're still friends. Harder to call her Puppy now because she's an old lady at this point. Also she reads this blog so now I'm in big trouble.

As for me, I've been called Robert, Rob, and Bob. Somehow never Bobby, at least as far as I can recall. Also some things less flattering. Doesn't bother me, though, because if you show that you're bothered by a nickname, that just makes them want to use it all the more. But really, I don't care; when I refer to myself in the third person here, I use Waltz. As long as I know it's me you're talking about, then whatever.

Some of those aren't what I'd normally think of as nicknames, though; just lazy versions of my name. Technically, Bob is a nickname, as is Ed and Liz and other common monikers, but I'm talking about how I perceive it, not the technical definition. A nickname is something like Wormy, above (I've never actually known anyone named Wormy, though I've known a couple of Zacks). Or Stinky, or Hoss (I live in the south), or Red.

Nicknames are also distinct from usernames, though it is of course perfectly acceptable to use a nickname as a username or, here, as a handle. I don't consider jackhammer69 to be a nickname, for example (or a particularly clever username). Unlike with usernames, usually you don't get to choose a nickname for yourself, but you can end up owning it if people call you it.

Interesting thing about French I've learned: it's fairly common knowledge, I think, that the French word that translates as name is nom. The translation of first name is prenom. But there's also a French word, surnom, that you'd think would mean surname or, as we think of it in English, family name; but no, nom means either surname or full name (I'm still a little unclear on the usage), while surnom translates to nickname. Which is especially weird to me because the French word sur generally means something like on, or on top of, as in sur la table. It may well be a linguistic coincidence, but to remember it I started thinking of surnom, nickname, as meaning above the name.

But the really cool thing about nicknames is that, well, they're usually bestowed upon someone once their character is at least somewhat developed, as opposed to one's legal name, which is usually granted before or just after birth, before your parents know what you're really going to be like. While it could be argued that given names can steer one's personality and guide one's career - you think John Wayne would have had the gravitas he did if he'd kept Marion Morrison as a working name? -- the reverse can be true for nicknames.

The downside of nicknames is, of course, that kids are assholes and they'll come up with embarrassing ones, like for example calling someone named Amber "Amberger."

With all the power names have, you'd think there'd be more people choosing them for themselves. I guess in most cases, you're either used to the one you're stuck with at birth, or you want to respect your parents' choice. Besides, changing it can be a real pain in the tuchis. And that can sometimes lead to ridicule, too, as when Prince changed his name to an unpronounceable symbol.

Bottom line is, usually I'll call a person by the name they wish to be called. Anything else is just rude.

Unless you're Puppy.

It has come to my attention that y'all voted this Best Blog for the second year running. All I can say is: thank you. I appreciate the votes, the readers, and of course the comments. But definitely read the other nominations, too; they're worth the time. And congratulations to all the other Quills winners!

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