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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 10 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

November 1, 2021 at 12:02am

#1020504

Bare Necessities

Well, it's November. Two more months until the end of the year. Somewhat less than that and, if nothing catastrophic happens, I'll have written in this thing every day for two years. Hey, I don't have many accomplishments in life; give me that one.

For those of you peeking in for the first time from the November edition of "30-Day Blogging Challenge ON HIATUS"

[13+]: Hi, I'm Waltz. This is my blog. I'm a dedicated indoorsman and I live an alcohol-positive lifestyle.

PROMPT November 1^st

We all have possessions of some type. Tell us five possessions you can’t live without, and why they are on this list.

I'm just going to go ahead and assume this is metaphorical and not literal, otherwise everyone would be like "air, water, food, clothing, shelter," and that would be boring. I'm also going to exclude consumables such as beer, which is only in my possession for a few minutes before it becomes a part of me; and also semi-sentient entities such as cats and friends. But the funny thing about possessions is that, often, we think we can't live without them but it turns out life goes on when they break, someone steals them, or they run into a deer and get totaled. So without further ado, The Five Possessions I Can't (Or, Technically, Wouldn't Want To) Live Without.

5. House

Yeah, yeah, I know, that's part of the "shelter" necessity above. But while "shelter" in general may be a necessity for human life, I'm talking about my house in particular. I acquired it half a lifetime ago, and it's paid off, so it really is my possession. It's about the right size for me and a housemate and the cats; the location is terrific (I can easily walk to at least four different bars and stagger back); and it usually doesn't leak. While I love to travel, I don't think I'd be happy living anywhere else for an extended period.

4. Laptop

I spend most of my waking hours on the laptop -- writing, working, learning shit, playing video games, watching shows and movies, laughing at cat videos. I could probably get by without my dumbphone, but not the laptop. It's getting old now and probably needs to be replaced soon, at which point the new laptop will be what I can't live without. In other words, it's not necessarily this computer, but a computer that I need to lead a fulfilling life.

3. Chair

Really, almost any chair will do as long as it's not too uncomfortable. A chair is essential for #4 above. Standing while using the computer would get really old really fast.

2. The Bed

When I'm not on my laptop (or at a movie theater or bar), I'm in the bed. It's comfortable and adjustable so I can sit up and read in it. Since I spend at least a third of my life there, it makes the list.

1. Money

Of all the things on this list, this is the most important (hence its position at #1; I'm stealing the format from Cracked here and doing the whole countdown thing). Why is it the most important? Obviously, because if I ever found myself in the position of being without any of the above things, or the 99,996 other things I don't want to live without, money would be there to replace it. So really, of all the things on this list, it's the one thing I truly can't live without.

"But Waltz, money can't buy happiness!" Maybe not, but it can buy beer, and that's good enough for me.

There are, of course, myriad other items that could have made the list: books, water heater, stove, toilet, refrigerator, washer/dryer, plunger, shower curtain, sunglasses... life would be annoying and/or boring without a lot of that stuff. And this is one reason why I am not, and don't think I ever could be, a minimalist.

I have managed to live without a car for four months now, though, so you never know.

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