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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 19 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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This is a private area. Access has been restricted and you may not view it under its current settings. If you feel you should have access, please contact the area's owner and request access.

Note: To contact a member via email, click the small envelope icon to the right of their handle. You must be logged into your account to send an email.

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

November 5, 2024 at 10:17am

#1079535

Anomalies

Ah, yes, November 5, and Election Day in the US. The UK will be celebrating an attempted terrorist attack, while over here, we're trying to avoid a terrorist attack.

The Random Number Gods have chosen to bless us with another Cracked link today.

5 Spots on Earth Where the Laws of Physics Fall Apart
There’s a gravity hole in the ocean

Okay, but, no, there are no spots on Earth where the laws of physics actually fall apart. Well, maybe, sometimes, at CERN, but they do it on purpose.

Still, these are rather interesting.

There are some places on the planet where things get weird. For instance, you ever heard of the Bermuda Triangle? Well, it turns out there’s nothing weird about that bit of the ocean at all — it sees a lot of traffic, but vessels that travel there are no more at risk than those anywhere else.

Like Bigfoot, that's not going to stop humans from making shit up about it.

5 Gravity Drops Near Sri Lanka

Once you learn that the force of gravity is slightly variable across the planet, it stands to reason that there are some spots where it's less and others where it's more. Finding out where it's less, though, that's what science does.

Gravity varies from place to place — and in some places, it varies a lot. In the ocean near Sri Lanka, gravity is so much weaker than in the rest of the world that the sea level is more than 300 feet lower than it would otherwise be.

Hey, I just came up with a fix for rising sea levels! Just increase the gravity of the Indian Ocean, and presto!

To know why gravity’s so low there, we’d have to burrow deep into the planet, and possibly cut it in two, which is inadvisable.

Awww.

Now, look, what that article's not telling you is that it's a minuscule effect. The variation from average, above or below, is about 0.5%. We'd never feel it. Sure, it has a profound effect on sea level, but look at what the comparatively really very tiny effect of the Moon's gravity does to that on a daily basis.

4 The Toasty Bit of Norway

In the Norwegian Sea, we have one disturbing bit called the Lofoten Vortex, where the water stores an unusual level of heat.

Lofoten Vortex can be the name of my Bjork cover band.

Yes, yes, I know Bjork is from Iceland, but come on, look at a globe. (A flat map inevitably distorts the distance between Iceland and Norway.)

3 On Top of Paraguay, Magnetism Disappears

I recently saw an argument for why the Earth's magnetic field isn't as important as we thought for maintaining our atmosphere. But this isn't about that.

Without looking at the map, if you had to guess one spot where the magnetic field gets weird, maybe you’d point your finger at one of the poles. But the planet’s rotational axis, which defines where we put the north and south poles, isn’t the same as its magnetic axis (which creates the magnetic field). As a result, we have this belt of radiation around the globe that dips down and comes close to us at this unlikely spot above Paraguay.

So, it doesn't "disappear." It just gets weaker there. How much weaker, I can't be arsed to look up. I can forgive a comedy site for hyperbolic headers, but they made it sound like, I don't know, compasses won't work in Paraguay or something.

2 The Tulsa Center of the Universe

You might not have known that the center of the universe is in Tulsa, but that’s what this spot is named, and Oklahoma wouldn’t lie to us.

Can't be the center of the universe; I don't live in Tulsa.

We’d go investigate ourselves, but that would mean having to spend time in Tulsa.

Good reason.

1 The Cave Where Energy Comes from Rock

I mean, technically, coal is rock. Uranium ore is rock.

But then you have Movile Cave in Romania. The interior is totally cut off from the outside world, and the creatures in there get no energy through photosynthesis, either directly or indirectly. Instead, the producers of this food web are bacteria that get their energy through chemosynthesis.

Here, though, they're talking about an entire cave ecosystem that doesn't rely, at its base, on solar energy input (apart from, you know, it not being frozen solid and all). Which is outside our normal experience, and definitely doesn't break the laws of physics any more than the other examples do, but is really interesting. Because now we know for sure that life can exist without photosynthesis.

Exist, yes, but imagine crawling out of that cave to go vote. Who are the candidates, now?

3 Like • Comment • View 2 comments

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