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Saturday, Nov. 16, 2024

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

a day 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

a day 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.

November 23, 2021 at 12:01am

#1022175

Gelotology

I don't really have a favorite joke. Jokes depend on circumstances, context, and audience.

PROMPT November 23^rd

In your blog today, tell us your favorite joke. It can be long, short, it does not matter. What makes this particular joke your favorite one? C'mon, show us your sense of humor!

While I don't have a favorite joke, there are a few I remember from the days, pre-internet, when it was important to remember jokes because you couldn't just look them up by Googling the punch line.

Of those few, a couple stick out because they elicit the best responses from the audience. Sometimes that response is hearty laughter, and that's fine. But sometimes, it's... well, let's just say I make sure they're not holding anything lethal when I tell them.

There are a few versions of this one circulating. I'm not going to look any of them up, but I'll tell it my way. Also, I'm pretty sure I've typed it in here before, but I can't be arsed to look that up, either. Likely I told it differently before. That's how jokes are supposed to work, you know; there's not one "official" version, but they mutate over time.

So this scientist was working hard, researching a way to vastly extend the lifespan of marine mammals. One of the important ingredients in the serum was extract of mynah bird.

One day, while at a critical stage in the serum's development, testing it on his pet dolphin, he ran out of mynah bird extract. So he set out to the pet store to replenish his supply. While he was gone, though, there was a problem at the city zoo; some of the big cats escaped. The biggest cat of all ended up wandering around until he curled up on this scientist's doorstep.

So he comes home, bag full of mynah birds in hand, but stops up short when he sees the King of the Beasts, right there on his doorstep, sleeping soundly.

"Oh man," the guy thinks to himself. "Oh, no, what am I going to do? I have to get inside. I'm at a critical stage in my experiments! There's no other way into the house, and I sure don't want to wake him up."

So he thinks about it for a few seconds, then starts sneaking up to the sleeping beast, ninja-like, tiptoeing as quietly as he possibly could. He gets one foot over the animal when suddenly a dozen cops appear out of nowhere, guns drawn.

"Freeze, mister!" they call. "You're under arrest...

...for transporting mynahs across sedate lions for immortal porpoises!"

And that's why I need to make sure there's nothing sharp or heavy in the vicinity when I tell it. That's also why it's one of my favorite jokes: I get to laugh at the audience's pain, and pain makes the best humor.

Regarding the title, gelotology

is the study of laughter. Not to be confused with Jellotology. In fact, I don't know how to pronounce the G. I'm going to go ahead and assume it's a hard G like in gif, not a soft G like in Georgia.

5 Like • Comment • View 8 comments

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