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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:

Elisa the Bunny Stik

about 7 hours ago
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

August 17, 2020 at 12:08am

#990991

The Real You

And who, exactly, do you think you are?

https://www.cracked.com/article_27124_totally-random-things-that-make-you-well-y...

Totally Random Things That Make You, Well, You

Let me get this out of the way: These are not "totally random." Yes, yes, I know, I'm quibbling about the definition of "random" when talking about a dick joke site.

6. Your Eye Color Can Determine Your Alcohol Tolerance ... And Propensity For Alcohol Addiction

When the time comes for drinking, some of us can down eight shots and still beat anyone in the bar at blindfolded darts, while others have to be carted home after sniffing a single beer-soaked napkin.

And some of us don't play drinking games. But I guess I'm a bit older than Cracked's intended demographic.

Blue-eyed people consistently hold their liquor better than those of us with brown-eyes.

Well, that explains everything (I have blue eyes).

Blue-eyed folk's high tolerance seems to put them on track for drinking more and for ultimately being more likely to become alcoholics.

If I'm not one by now, I never will be. If by "alcoholic" you mean "anyone who drinks," then sure.

Whatever the explanation, people now know simply by looking at you how easily they can get you drunk, which is why, personally, we recommend wearing sunglasses at all times.

That also helps to hide the dilated pupils and the red sclera. And mutes the hue of the pink elephants.

5. Having A "Normal" And Easy-To-Pronounce Name Can Make You More Likable And Successful

Students with common names tended to succeed more than their weird-named counterparts, while the ones with the uncommon names were the ones most likely to have psychological problems.

Okay, here's the thing: I'm painfully aware that this sort of thing has racist (or at least cultural) ramifications. It's been shown that identical resumes, where one applicant was named, like, "Steve" and another named, like, "Hamal," led to the former being accepted and the latter rejected, more times than not. At least in the US. So I don't really like the way this section is presented.

But that's no excuse for anyone to name their kid Kaiyleeighh. There is, in fact, no excuse for that at all.

4. Have A Bunch (Or Very Few) Friends And A Huge (Or Tiny) Social Network? It's Probably Your Gut Bacteria

You're on the internet and reading a humor article, so there's a fair chance you call yourself an introvert.

How... how did you know?

What made you that way? Was it your upbringing -- your parents took you to one party when you were three, and it was so loud and sticky that you swore off people forever? Is it in your genes -- your parents were both introverts, and it's frankly amazing that they even socialized enough to ever meet each other? Maybe it's both those, but there could be other factors too. Ten trillion of them in fact, and they're living in your intestines.

I'm starting to get the impression that this is the bacteria's body, and I'm just living in it.

3. The Air Quality In Your Home And School Probably Determined How Intelligent You Are

In 2015, Southern California experienced a gas leak that was absolutely huge -- you can't really compare gas leaks to oil spills, but if you could, this leak would be bigger than 2010's Deepwater Horizon disaster. People around Los Angeles got pretty worked up about the thousands of tons of methane and other gases suddenly hissing around them, and they responded by installing air purifiers in schools, places where sudden emissions of methane are otherwise normally just a source of comedy.

A year later, test scores in schools with the new air filters (and only those schools) went up, measurably.

One data point does not a conclusion make, but the article goes on to point out that, yes, it's happened in other places too.

Every study on a more specific group comes up with the same thing. Baseball umpires? Chess players? Pear pickers? Everyone gets dumber as the air gets dirtier.

Which explains so much.

2. Your Birth Weight Partially Determines Your Respiratory And Cardiovascular Fitness As An Adult

Speaking of respiration, your respiratory prowess might have been set from the moment you were born. And sure, a lot of things are set at that point, that's kind of how genes work, but in this case, your parents were able to view your hidden settings using something clearly observable from the start. We're talking about birth weight, which is approximately the first thing the nurses check when you're born, right after what kind of genitals you're packing and whether you have a tail.

Pretty sure the first thing they check is if you're squirming or not, but whatever.

Obviously, you're still able to change your heart and lung health by exercising, and you should really get on that. Just know that the game is slightly rigged from the start. And when you have a baby of your own, make sure to weigh them immediately and take a commemorative photo with them hanging from a scale at the dock.

Trophies are trophies, after all.

1. Your Facial Features And Tone Of Voice Can Determine How Much You Care About The Environment

One fun thing psychologists like to do is think of some idea that kind of feels like it could be true, put together a study to see if it's true, and then cackle in delight when they find that, whoa, it's true.

And then get mad when another team of psychologists can't replicate the experiment and accuse the first team of p-hacking.

Like what happened last year when a Canadian team wondered, hey, you know how research says that the more masculine a man looks, the more selfish and violent he in fact turns out to be?

The obvious problem with this is that "masculinity" is subjective.

The subjects then answered an environmental survey, and the more noticeably masculine guys gave answers indicating that they didn't care much about the environment at all. The researchers had a pretty clear explanation handy. This all came down to testosterone.

Ummm... what? No, it's more likely due to socialization of gender roles.

So what does that mean? Was this whole study a bunch of bullshit? Maybe, or there could be another factor here: the socialization of gender roles.

Aha! Confirmation!

Anyway, as always, don't take anything from Cracked as Truth. I just think the whole thing's interesting. Or, rather, my gut bacteria think it's interesting and made me type this. Help I'm a prisoner in someone's colon!

5 Like • Comment • View 3 comments

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