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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:

Kåre Enga in Udon Thani

about 24 hours ago
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

about 24 hours ago
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

about 24 hours ago
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

a day ago
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

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

September 7, 2020 at 1:30am

#992611

You CAN Take It With You

What is this "productive and happy" of which you speak?"

PROMPT September 7th

I completely rearranged my desk space yesterday! It was a much-needed change and has helped with my motivation. What does your desk space / writing space look like? What sorts of things do you need (or not need) in your work space to be productive and happy?

Here's the thing: I like being in a clean, organized space.

Here's the other thing: I despise cleaning and organizing with every fiber of my being.

These two urges tug constantly at my psyche, just like "eating that whole pizza" vs. "not having another heart attack." Sometimes one wins. Sometimes the other does. Most of the time I just distract myself with something else.

Anyway, I don't have dedicated desk space right now. My office has gathered too much crap, and I can't be arsed to straighten it all out. I write on a laptop, because a) I travel, or I used to in the Before Time, and b) I like to sit outside on my deck whenever it's not too cold. Too hot, I can deal with. Drop below about 70F / 21C, though, and I start to freeze to death.

I'm not looking forward to fall and winter.

Anyway. it's a honkin' big laptop, because I also use it for gaming. Not light, and I've seen cinderblocks smaller than the size of the power converter. Still, it's portable enough to fit into my backpack for travel, if that ever becomes an option again, and no one wants to steal the backpack because it's heavier than a box of rocks.

One of the things I like most about traveling is hotel rooms.

I know this is probably just as unrelatable to most people as my desire for heat over cold. Hotel rooms freak a lot of people out. Me? Love 'em. Even the dingy, faded ones. I've been in those, and I've also stayed at the actual Ritz-Carlton. And everything in between. Because I walk into one, and it's sparse: A bed or two. Bathroom. A nightstand with a lamp. A dresser. A desk and chair. A TV which I utterly ignore. One of the reasons I don't usually travel with people is every time I do, they seem to have this need to walk into a hotel room and immediately turn the TV on. It's annoying as hell and I don't understand it. All TV can do is provide us with commercials and other chaotic noises.

But I digress. A hotel room looks clean and neat. It may not actually be clean, but I don't give a damn. Best of all, I'm not the one who cleaned it. I pay for that privilege gladly. So then I can set up my excessively-sized laptop on the desk, plug it in, and game, or write, or look at cat videos, or whatever.

Now, look, I don't want to give anyone the idea that I'm a lazy bum who expects other people to do his housework for him. No, I'm a lazy bum who hates to do housework, and hates even more if someone does it for me -- except in the aforementioned hotel rooms. I neaten up when I have to at home, but not before. Usually I just take the laptop outside, as I said, where I can't leave a lot of shit lying around because sometimes it rains, snows, or winds.

Productive and happy, though? Pipe dreams.

Final Birthday Week MB goes to WakeUpAndLive️~🚬🚭2024

as a fellow Trekker, but please know that I appreciated all of the comments. Yes, all of them. Thank you. Some things coming up this week: Tomorrow is Star Trek Day, which commemorates the anniversary of the first airing of the first Original Series episode on September 8, 1966; September 10 would have been my father's 103rd birthday; and then September 11 is, among other things, my account anniversary. Hopefully I'll remember to give out more Merit Badges for my account anniversary, if I don't drink too much rum the day before (Dad was a sailor).

8 Like • Comment • View 10 comments

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