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Complex Numbers

by Waltz Invictus

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:

Annette

about 11 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

June 30, 2024 at 7:40am

#1073352

Revisited: "Rock you like a..."

Today's retrospective takes us back to September of 2018, a brief entry about the weather: "Rock you like a..."

So now, six years less a season later, how have things changed?

It's hard to avoid people talking about the impending doom of Hurricane Florence, so I might as well add my voice to the babble.

I remember that one. While it hit the coast as a Cat 1, it was so slow-moving that what it lacked in wind damage it made up for in massive flooding.

No, I'm nowhere near the coast. Looks like the worst we'll get is a bunch of rain. Nothing new there; it's been raining more often than not all summer. I'm at a high spot and I have a sump pump and a backup generator.

I swear my sense of time is horribly distorted. If you asked me yesterday when I got my generator, I'd have probably answered, "I don't know. 2020, maybe?" Our power sometimes goes out in a light breeze, so it's not just for hurricanes. I justify the presence of the (very loud) generator by claiming I have a medical device that requires electricity, which is true, but the main reason is I don't want to be without internet for more than five minutes.

I also have a house surrounded by trees, though, so I might be boned anyway.

Since then, I've had at least one of the trees taken down, one that was leaning noticeably toward the house. Still boned when the next 'cane blows through.

Some good friends of mine live in Raleigh, NC. They're boned.

They got through it just fine. Couldn't go anywhere for a day or so, if I recall correctly, but safe and dry. They just bought a house in southwest Virginia this year, which means the next hurricane will head for them. And yes, hurricanes can still do significant damage that far inland. Not as often, but it happens.

I have a fondness for Virginia Beach and the Outer Banks. I'll miss them.

My fondness for Virginia Beach ended when I heard that my favorite watering hole there was closing. And miraculously, most of the OBX is still there. I just spent a night there last year.

It seems like a lot of the places I've been to have been hit by something.

Some sort of familiarity bias. Also, I travel more than a little, and every time I do, the chance of a place I've been getting smacked by some disaster goes up a little.

Well, as long as Las Vegas is still- wait, what? The Colorado River is at historic low flows, and Lake Mead is dangerously dry?

Since then, the water level there has fluctuated,

but it's still pretty low. I also haven't been to Vegas since the pandemic started.

I'd ship 'em some of our rain if I could. Let me tell you, if I ever hear another breath about "drought" around here, I'mma lose it at someone.

We've had a bit of a dry spell this year (I write this during a drizzle, however, and we're supposed to get thunderstorms this afternoon and evening). My grass is partly brown. Good thing I don't live in an HOA; I refuse to waste water on lawn irrigation.

They've been predicting a very active hurricane season this year, but those long-range predictions are questionable at best, so I don't pay much attention to them. Weather is notoriously hard to predict with any accuracy more than a week out, so I'll do what I do every year: wait and see.

And try to remember to get my generator serviced.

1 Like • Comment • View 1 comment

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