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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Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 20 hours ago
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

about 24 hours ago
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

🌖 HuntersMoon

a day ago
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

a day ago
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
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

Dec 20, 2024 at 6:06pm
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

Dec 20, 2024 at 1:00pm
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

Dec 20, 2024 at 12:58pm
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

December 17, 2024 at 7:01am

#1081249

Need for Speed

Today, from the Land of Party Poopers (actually, from Thrillist):

No, That Isn't Duct Tape on Your Plane's Wings
An aircraft mechanic explains what the tape you sometimes see on plane wings really is.

Why Party Poopers? Well, because they're taking one of my few precious joys out of life.

See, I don't fly all that often. Once a year, maybe. (Okay, twice, if you count the round trip as two trips.) So I don't get to do this often, but when I see that tape on a plane, I usually wait until the plane starts to taxi away from the gate to loudly exclaim, "Hey, look, the wings are being held together by duct tape!"

I also find the fake outlets

at waiting areas incredibly hilarious, though I've never done that prank, myself.

Those are little moments of happiness for me, but this article sucks the joy out of the first one. Well, at least, it would, if people actually read Thrillist. Maybe my faux-freakout over the tape will still have its desired effect.

Anyway, after all that, I'm sure you're dying to know what it really is on the wings.

As a passenger, noticing that your plane's wings are seemingly held together by the same silver duct tape that your dad uses to fix anything around the house is, by all means, a frightening sight.

Or, you know, it would, if duct tape weren't so damn useful.

"That's not actually duct tape," says an aircraft mechanic in a TikTok video addressing the issue. "That's speed tape, [...] and speed tape is an aluminum-base tape that's designed specifically for aviation due to the large speeds and the large temperature differentials that aircraft are subjected to."

I actually knew that. But knowing that it's called "speed tape" doesn't help for shit. Like, from the sound of it, it should make the airplane go faster, but if that were the case, the whole plane would be covered in it, right? If it has something to do with the "large speeds" (eyetwitch) as well as temperature differentials, why call it speed tape and not cold tape?

Instead, sometimes, it's used as a temporary sealant to prevent moisture from entering specific components.

Uh huh. Okay. Doesn't tell me why it's called speed tape.

"Speed tape, also known as aluminum tape, is a material used for temporary, minor repairs to nonstructural aircraft components," an FAA spokesperson told Thrillist.

And it's called that because...?

Yes, I know I could ask some random AI the question and get some kind of answer, but that's not the point. The point is, why can't the article purporting to explain all about speed tape not even bother to explain why it's called speed tape?

You can relax now and enjoy your flight stress-free.

HA! Like there aren't 498 other things about flying that cause stress.

Oh, right: 499 if I'm around.

4 Like • Comment • View 4 comments

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