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Thursday, Apr. 25, 2024

10:27pm EDT

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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

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Show Recent Comments

10 Most Recent Blog Comments:

Kåre Enga in Udon Thani

about 19 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 19 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 19 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?

#2378. Oopsies
ID #1051896 entered on June 30, 2023 at 12:14am

#2377. Occupational Hazards
ID #1051820 entered on June 29, 2023 at 9:27am

#2376. The Second Mouse
ID #1051699 entered on June 28, 2023 at 9:21am

#2375. Jeté
ID #1051660 entered on June 27, 2023 at 10:01am

#2374. In the Game
ID #1051607 entered on June 26, 2023 at 8:54am

#2373. Revisited: "Put a Pin in This Synergy"
ID #1051555 entered on June 25, 2023 at 6:39am

#2372. Interval Training
ID #1051521 entered on June 24, 2023 at 10:07am

#2371. The Cat's Meow
ID #1051484 entered on June 23, 2023 at 11:03am

#2370. Art History
ID #1051447 entered on June 22, 2023 at 10:19am

#2369. Pas de Cheval
ID #1051413 entered on June 21, 2023 at 10:57am

#2368. Cereality
ID #1051373 entered on June 20, 2023 at 10:47am

#2367. Unplanned Obsolescence
ID #1051306 entered on June 19, 2023 at 8:22am

#2366. Revisited:"Nothing's unforgiven in the four corners of Hell"
ID #1051216 entered on June 18, 2023 at 9:15am

#2365. Everything, Everywhere...
ID #1051171 entered on June 17, 2023 at 9:25am

#2364. (As an Aside...)
ID #1051135 entered on June 16, 2023 at 10:27am

#2363. Strength
ID #1051095 entered on June 15, 2023 at 10:29am

#2362. Mythinformation
ID #1051050 entered on June 14, 2023 at 9:43am

#2361. A Whole Lotto Nonsense
ID #1051013 entered on June 13, 2023 at 8:09am

#2360. Swimming
ID #1050969 entered on June 12, 2023 at 9:07am

#2359. Revisited: "Amazon"
ID #1050930 entered on June 11, 2023 at 9:57am

#2358. sWords and Sorcery
ID #1050891 entered on June 10, 2023 at 9:08am

#2357. Plie
ID #1050848 entered on June 9, 2023 at 7:44am

#2356. Staten Island? Yes, It Is.
ID #1050787 entered on June 8, 2023 at 7:55am

#2355. Choice Responses
ID #1050744 entered on June 7, 2023 at 11:59am

#2354. Cardio
ID #1050685 entered on June 6, 2023 at 7:07am

#2353. Driving a Semicolon
ID #1050592 entered on June 5, 2023 at 9:21am

#2352. Revisited: "I'm in Hell."
ID #1050559 entered on June 4, 2023 at 9:28am

#2351. Pole Vault
ID #1050476 entered on June 3, 2023 at 9:03am

#2350. Powerless
ID #1050418 entered on June 2, 2023 at 10:14am

#2349. Stop Making Sense
ID #1050375 entered on June 1, 2023 at 11:41am

#2348. It's Not Right
ID #1050318 entered on May 31, 2023 at 9:22am

#2347. Shit on a Single
ID #1050264 entered on May 30, 2023 at 7:57am

#2346. What You Wish For
ID #1050227 entered on May 29, 2023 at 10:40am

#2345. Revisited: "Poor You"
ID #1050188 entered on May 28, 2023 at 9:35am

#2344. Ur Gent
ID #1050145 entered on May 27, 2023 at 11:37am

#2343. Thirty Years After
ID #1050116 entered on May 26, 2023 at 11:34am

#2342. Uncomfortably Numb
ID #1050071 entered on May 25, 2023 at 8:45am

#2341. Machine Learning
ID #1050033 entered on May 24, 2023 at 7:52am

#2340. Authenticity
ID #1049998 entered on May 23, 2023 at 10:06am

#2339. Thumbs Out
ID #1049962 entered on May 22, 2023 at 8:15am

#2338. Revisited: "Naturally"
ID #1049920 entered on May 21, 2023 at 9:03am

#2337. Setting Boundaries
ID #1049871 entered on May 20, 2023 at 11:37am

#2336. Every Thing
ID #1049836 entered on May 19, 2023 at 10:37am

#2335. Legally Binding
ID #1049803 entered on May 18, 2023 at 6:11pm

#2334. Some Time
ID #1049703 entered on May 17, 2023 at 8:14am

#2333. A Frank Discussion
ID #1049662 entered on May 16, 2023 at 9:47am

#2332. Extinct
ID #1049626 entered on May 15, 2023 at 9:21am

#2331. Revisited: "Something about Nothing"
ID #1049580 entered on May 14, 2023 at 9:27am

#2330. True or False: Nutrition Edition
ID #1049551 entered on May 13, 2023 at 8:22am

#2329. Mind, the Gap
ID #1049518 entered on May 12, 2023 at 8:06am

#2328. Divided by a Vulgar Language
ID #1049467 entered on May 11, 2023 at 10:04am

#2327. Free
ID #1049425 entered on May 10, 2023 at 10:35am

#2326. Alarming Trend
ID #1049389 entered on May 9, 2023 at 11:24am

#2325. Fair Morning
ID #1049353 entered on May 8, 2023 at 9:07am

#2324. Revisited: "No Fault of Mine"
ID #1049327 entered on May 7, 2023 at 9:42am

#2323. Enter the Dragon
ID #1049296 entered on May 6, 2023 at 1:18pm

#2322. A Sentence Walks Into a Bar, Comes To a Full Stop
ID #1049238 entered on May 5, 2023 at 11:40am

#2321. Lichen Thropy
ID #1049209 entered on May 4, 2023 at 1:06pm

#2320. For a Lark
ID #1049152 entered on May 3, 2023 at 9:01am

#2319. Outer Limits
ID #1049120 entered on May 2, 2023 at 12:44am

#2318. Going South
ID #1049063 entered on May 1, 2023 at 12:51am

#2317. Revisited: "Asking Persimmon"
ID #1049023 entered on April 30, 2023 at 3:38am

#2316. Stuck in Committee
ID #1049011 entered on April 29, 2023 at 8:26pm

#2315. That's Better
ID #1048945 entered on April 28, 2023 at 2:58pm

#2314. Pushing My Buttons
ID #1048899 entered on April 27, 2023 at 5:26pm

#2313. Get the Lard Out
ID #1048815 entered on April 26, 2023 at 7:23am

#2312. That Newfangled Junk
ID #1048752 entered on April 25, 2023 at 9:56am

#2311. It's In My Genes
ID #1048696 entered on April 24, 2023 at 9:50am

#2310. Revisited: "Cryptonite"
ID #1048643 entered on April 23, 2023 at 8:59am

#2309. But the Sun Is Eclipsed By the Moon
ID #1048605 entered on April 22, 2023 at 9:55am

#2308. Boned
ID #1048554 entered on April 21, 2023 at 11:26am

#2307. Heavy Size
ID #1048496 entered on April 20, 2023 at 9:24am

#2306. Just One Word
ID #1048454 entered on April 19, 2023 at 10:57am

#2305. Unknown
ID #1048384 entered on April 18, 2023 at 10:09am

#2304. In-Vesting
ID #1048319 entered on April 17, 2023 at 9:16am

#2303. Revisited: "Calvin Tribute"
ID #1048283 entered on April 16, 2023 at 9:53am

#2302. The Less You Know...
ID #1048245 entered on April 15, 2023 at 10:36am

#2301. I Ain't Got a Thing...
ID #1048188 entered on April 14, 2023 at 11:31am

#2300. Urine Trouble
ID #1048137 entered on April 13, 2023 at 1:43pm

#2299. Charmeuse
ID #1048059 entered on April 12, 2023 at 9:22am

#2298. Word to the Wise
ID #1048020 entered on April 11, 2023 at 10:16am

#2297. Hem
ID #1047949 entered on April 10, 2023 at 10:29am

#2296. Revisited: "Once More With Feeling"
ID #1047885 entered on April 9, 2023 at 12:02pm

#2295. Uncivil
ID #1047803 entered on April 8, 2023 at 10:40am

#2294. Sweater
ID #1047729 entered on April 7, 2023 at 1:27pm

#2293. Mind Your Own Mind
ID #1047614 entered on April 6, 2023 at 7:51am

#2292. Portrait of a Rant
ID #1047527 entered on April 5, 2023 at 8:56am

#2291. Only the Lonely
ID #1047477 entered on April 4, 2023 at 11:46am

#2290. Difficulty
ID #1047419 entered on April 3, 2023 at 11:03am

#2289. Revisited: "Judge, Mental"
ID #1047344 entered on April 2, 2023 at 10:25am

#2288. Lost in Thought Experiments
ID #1047267 entered on April 1, 2023 at 12:25am

#2287. Being a Pill
ID #1047230 entered on March 31, 2023 at 10:45am

#2286. Can't Get There from Here
ID #1047161 entered on March 30, 2023 at 7:10am

#2285. Acts of Kindness
ID #1047132 entered on March 29, 2023 at 12:09pm

#2284. Measure by Measure
ID #1047081 entered on March 28, 2023 at 9:39am

#2283. On the Bias
ID #1047040 entered on March 27, 2023 at 10:06am

#2282. Revisited: "Invincible"
ID #1047009 entered on March 26, 2023 at 12:46pm

#2281. Attention Payment
ID #1046966 entered on March 25, 2023 at 11:03am

#2280. Advisory
ID #1046915 entered on March 24, 2023 at 9:31am

#2279. Unnatural
ID #1046875 entered on March 23, 2023 at 10:35am

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