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Tuesday, Jul. 2, 2024

12:20pm 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:

tracker

about 3 hours ago
In response to "Imma Let You Finish, But..."

I am a sports fanatic!!!! You will see more of me.

1 Like

tj ~ endeavors to persevere!

a day ago
In response to "Revisited: "Rock you like a...""

I also purchased a generator because our power would go out anytime the wind blew. It seems to have worked, we seldom have power outages now. Living in Minnesota, all we get when the hurricanes push threw are thunder storms and rain. But, it's Minnesota, so thunder storms and rain are normal. This year does seem to be rainier, however.

I'm thinking, after reading this, that I should invest in a couple of rain barrels and bottle the water up. I could probably sell it online to drought stricken people.

1 Like

Kåre Enga in Montana

Jun 29, 2024 at 2:16pm
In response to "Je Voyagerai"

I once was allergic to going on a cruise. But... I should... just for the experience. I've gotten out of my comfort zone for experience.

With the crush of tourists these days any travel should include how much you want to put up with "other people's vacation" as opposed to your own.

1 Like

Lazy Writer est 4/24/2008

Jun 29, 2024 at 1:38pm
In response to "Je Voyagerai"

Happy traveling..be safe.

Elisa: Middle Aged Stik

Jun 29, 2024 at 11:12am
In response to "It Ain't Wrong"

Ain’t apparently begins as amn’t, a contraction for am not, which you can still hear in Ireland and Scotland today

I mean, an abundant number of Scotch and Irish immigrants ended up in the American South, so this tracks.

While a lot of people consider ain’t improper, it’s a very regular and legitimate part of many forms of English, including in Black English (AAVE). Be mindful that judging someone’s use of ain’t as “wrong” can be a very socially loaded act, to say the least.

For some reason, this reminds of one of the reasons I stopped reading Ask A Manager. A bunch of people were getting real uppity about the use of the phrase "baby daddy". Unsurprisingly, many of these people appeared white. One Black person in the comments finally had enough and threw down with this remark:

"I gotta say, as a black woman it grates to have phrases that come out of AAVE be appropriated, assigned negative connotation (likely because they come from black culture), then discarded with prejudice. If you’re using the phrase to conjure up stereotypical imagery, I can get on board with putting an end to that. But there are plenty of people for whom baby daddy or baby mama are not pejorative at all, just descriptors of the relationship in their dialect, and correcting them to “Father of my child” is just another case of denigrating minority speech patterns and legitimate AAVE grammatical constructions and upholding “white is right” standards."

(For more context, check out this link

1 Like

🌕 HuntersMoon

Jun 28, 2024 at 10:54am
In response to "It Ain't Wrong"

Ain't you on a roll today...

3 Like

Adherennium Dr of Phoolishness

Jun 27, 2024 at 11:53am
In response to "Wave Rider"

Horrifying fact, I once painted a reproduction of the Hokusai wave on our bathroom wall. Eventually of course it was painted over, but I like to fantasise that in some distant future it will be archaeologically excavated and held up as an example of early cultural appropriation, (badly executed too.)

1 Like

Annette

Jun 26, 2024 at 8:16pm
In response to "The Oz Hypothesis"

The nekked wimmin look like something that I might have drawn in first grade.

1 Like

Aiva Raine

Jun 25, 2024 at 10:16pm
In response to "Can't Spell Success without Sucs"

Ok- this made me truly LOL- "sipping a gin and tonic made with low-paid laborer tears"

Thank you. Totally agree with the rest of your article.

Money doesn't solve all problems but it sure as hell eliminates many and makes it easier to go places or buy things that can create some happiness. IE- a property somewhere quiet and peaceful and a trailer with which to chill on said property.

Rich people are typically clueless assholes.

1 Like

Anni Pon

Jun 25, 2024 at 9:30am
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

2 Like

#2446. The Big One
ID #1055247 entered on September 6, 2023 at 8:29am

#2445. The Man, The Myth, The Reality
ID #1055201 entered on September 5, 2023 at 3:20pm

#2444. Astronomy
ID #1055136 entered on September 4, 2023 at 10:43am

#2443. Revisited: "Cold Hands, Cold Heart"
ID #1055066 entered on September 3, 2023 at 6:09am

#2442. Faded Genes
ID #1055015 entered on September 2, 2023 at 9:48am

#2441. Let's Settle This Like Men
ID #1054947 entered on September 1, 2023 at 11:11am

#2440. Pasta Prime
ID #1054900 entered on August 31, 2023 at 11:27am

#2439. The Problem of Stupid
ID #1054851 entered on August 30, 2023 at 9:20am

#2438. What's Wrong Ain't Right
ID #1054797 entered on August 29, 2023 at 9:58am

#2437. Law of Rules
ID #1054756 entered on August 28, 2023 at 11:47am

#2436. Revisited: "Larry Flynt is a Better Man than I Am"
ID #1054708 entered on August 27, 2023 at 9:40am

#2435. Ad Nauseam
ID #1054669 entered on August 26, 2023 at 9:15am

#2434. Symbol Minds
ID #1054570 entered on August 25, 2023 at 8:13am

#2433. Cool It
ID #1054518 entered on August 24, 2023 at 8:39am

#2432. Sumer Time
ID #1054477 entered on August 23, 2023 at 8:11am

#2431. Boregon Trail
ID #1054434 entered on August 22, 2023 at 10:23am

#2430. Meh. Whatever.
ID #1054398 entered on August 21, 2023 at 10:19am

#2429. Revisited: "Untruth and Consequences"
ID #1054349 entered on August 20, 2023 at 10:34am

#2428. In a Vacuum
ID #1054312 entered on August 19, 2023 at 10:11am

#2427. Boogie All Night Long
ID #1054270 entered on August 18, 2023 at 10:33am

#2426. The Seventh Planet
ID #1054219 entered on August 17, 2023 at 10:22am

#2425. The Time Machine
ID #1054180 entered on August 16, 2023 at 10:47am

#2424. Going to Prism
ID #1054138 entered on August 15, 2023 at 11:31am

#2423. What's the Big Idea?
ID #1054078 entered on August 14, 2023 at 10:00am

#2422. Revisited: "Enjoy this Christmas"
ID #1054040 entered on August 13, 2023 at 9:46am

#2421. Yosemitic
ID #1054000 entered on August 12, 2023 at 9:55am

#2420. Earth
ID #1053952 entered on August 11, 2023 at 10:30am

#2419. In Retrospect, These Were Bad Ideas
ID #1053910 entered on August 10, 2023 at 9:53am

#2418. Planet Ix
ID #1053868 entered on August 9, 2023 at 10:26am

#2417. Those Are Words
ID #1053806 entered on August 8, 2023 at 8:59am

#2416. Liquid Ick
ID #1053767 entered on August 7, 2023 at 9:11am

#2415. Revisited: "Finally!"
ID #1053717 entered on August 6, 2023 at 9:10am

#2414. Not What You'd Expect
ID #1053674 entered on August 5, 2023 at 9:33am

#2413. Leisure Seizure
ID #1053629 entered on August 4, 2023 at 10:28am

#2412. Warped Minds
ID #1053583 entered on August 3, 2023 at 10:45am

#2411. Coming to a Punderstanding
ID #1053488 entered on August 2, 2023 at 10:06am

#2410. Pretty Petty
ID #1053424 entered on August 1, 2023 at 9:35am

#2409. Underworld Underdog
ID #1053369 entered on July 31, 2023 at 9:34am

#2408. Revisited: "Pigs on the Wing"
ID #1053333 entered on July 30, 2023 at 9:39am

#2407. Getting the Drift
ID #1053258 entered on July 29, 2023 at 9:46am

#2406. Learn from the Best
ID #1053216 entered on July 28, 2023 at 10:24am

#2405. Basque in Its Glory
ID #1053111 entered on July 27, 2023 at 9:37am

#2404. It Ain't Wright, but It Ain't Wrong
ID #1053066 entered on July 26, 2023 at 9:33am

#2403. Á La Mode
ID #1053028 entered on July 25, 2023 at 9:15am

#2402. Millimeters of Mercury
ID #1052996 entered on July 24, 2023 at 9:14am

#2401. Revisited: "Best Waste of Time EVER"
ID #1052958 entered on July 23, 2023 at 8:26am

#2400. Smidgen Forge
ID #1052910 entered on July 22, 2023 at 8:48am

#2399. If You Cheese
ID #1052884 entered on July 21, 2023 at 11:57am

#2398. Mountains out of Mouse-hills
ID #1052836 entered on July 20, 2023 at 9:30am

#2397. Where We're Going, We Don't Need Rules
ID #1052795 entered on July 19, 2023 at 9:35am

#2396. Facts... In... SPACE!
ID #1052753 entered on July 18, 2023 at 9:37am

#2395. The Step-Parent of Invention
ID #1052714 entered on July 17, 2023 at 11:27am

#2394. Revisited: "Exercise"
ID #1052664 entered on July 16, 2023 at 7:59am

#2393. The Proverbial Trap
ID #1052625 entered on July 15, 2023 at 6:46am

#2392. Can I Have Two Words?
ID #1052589 entered on July 14, 2023 at 7:02am

#2391. You Realize This Means War
ID #1052549 entered on July 13, 2023 at 7:00am

#2390. Generational Drama
ID #1052515 entered on July 12, 2023 at 10:24am

#2389. If Only Things Were Different
ID #1052470 entered on July 11, 2023 at 9:47am

#2388. Write What You Write
ID #1052415 entered on July 10, 2023 at 9:34am

#2387. Revisited: "The Big Not So Empty"
ID #1052370 entered on July 9, 2023 at 8:25am

#2386. Unsung
ID #1052318 entered on July 8, 2023 at 7:27am

#2385. Thought for Food
ID #1052279 entered on July 7, 2023 at 10:24am

#2384. Pedalers
ID #1052229 entered on July 6, 2023 at 8:43am

#2383. Real and Complex
ID #1052191 entered on July 5, 2023 at 11:14am

#2382. No Fly Zone
ID #1052113 entered on July 4, 2023 at 12:33am

#2381. Another Fine Mess
ID #1052054 entered on July 3, 2023 at 2:36am

#2380. Revisited: "Epiphany"
ID #1051994 entered on July 2, 2023 at 12:03am

#2379. Moonshine
ID #1051940 entered on July 1, 2023 at 12:29am

#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

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