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Thursday, Jul. 4, 2024

3:18pm 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:

🌕 HuntersMoon

a day ago
In response to "A Bridge Too Far"

Just my opinion but I think he's lost his crown by being out-swindled by an even larger-than-life conman. Still a New Yorker, however, so the city still retains its reputation.

1 Like

tracker

Jul 2, 2024 at 9:08am
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!

Jun 30, 2024 at 11:01pm
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

#1448. Red and Redder
ID #1000093 entered on December 12, 2020 at 12:01am

#1447. Ring Out
ID #1000033 entered on December 11, 2020 at 12:01am

#1446. Resolve
ID #999970 entered on December 10, 2020 at 12:01am

#1445. Flaky
ID #999905 entered on December 9, 2020 at 12:01am

#1444. Do Not Want
ID #999846 entered on December 8, 2020 at 12:08am

#1443. Adventure Capitalism
ID #999783 entered on December 7, 2020 at 12:01am

#1442. Tradition!
ID #999730 entered on December 6, 2020 at 12:02am

#1441. XXI
ID #999667 entered on December 5, 2020 at 12:02am

#1440. Barbaric
ID #999616 entered on December 4, 2020 at 12:01am

#1439. Stuff and Nonsense
ID #999558 entered on December 3, 2020 at 12:01am

#1438. Frittered Away
ID #999502 entered on December 2, 2020 at 12:05am

#1437. Do I Dare To Eat An Apple?
ID #999441 entered on December 1, 2020 at 12:55am

#1436. December's Eve
ID #999376 entered on November 30, 2020 at 12:01am

#1435. Promptly
ID #999320 entered on November 29, 2020 at 12:01am

#1434. Wait, "Dust" Can Be A Verb Too?
ID #999252 entered on November 28, 2020 at 12:01am

#1433. I Want It Now
ID #999190 entered on November 27, 2020 at 12:07am

#1432. Gone Native
ID #999138 entered on November 26, 2020 at 12:03am

#1431. The One Unforgivable Sin
ID #999073 entered on November 25, 2020 at 12:02am

#1430. Serenity Now
ID #999003 entered on November 24, 2020 at 12:01am

#1429. Serial Skiller
ID #998936 entered on November 23, 2020 at 12:01am

#1428. Live On Stage
ID #998872 entered on November 22, 2020 at 12:11am

#1427. Aversion Therapy
ID #998795 entered on November 21, 2020 at 12:11am

#1426. Film Fest
ID #998739 entered on November 20, 2020 at 12:05am

#1425. Strangers in the Night
ID #998678 entered on November 19, 2020 at 12:01am

#1424. Original
ID #998616 entered on November 18, 2020 at 12:01am

#1423. Past Perfect
ID #998543 entered on November 17, 2020 at 12:01am

#1422. Survival
ID #998455 entered on November 16, 2020 at 12:01am

#1421. Good Enough
ID #998384 entered on November 15, 2020 at 12:01am

#1420. Epiphany?
ID #998322 entered on November 14, 2020 at 12:07am

#1419. We Just Disagree
ID #998246 entered on November 13, 2020 at 12:01am

#1418. Costumerism
ID #998176 entered on November 12, 2020 at 12:01am

#1417. Fast Food
ID #998107 entered on November 11, 2020 at 12:02am

#1416. Stylish
ID #998015 entered on November 10, 2020 at 12:07am

#1415. Sproing!
ID #997949 entered on November 9, 2020 at 12:02am

#1414. Adventure Time
ID #997877 entered on November 8, 2020 at 12:04am

#1413. Beauty's Snare
ID #997822 entered on November 7, 2020 at 12:02am

#1412. Gridlocked
ID #997752 entered on November 6, 2020 at 12:03am

#1411. Ten Years After
ID #997682 entered on November 5, 2020 at 12:01am

#1410. Run, Nose, Run!
ID #997646 entered on November 4, 2020 at 3:27pm

#1409. You Can't Deep End On Me
ID #997526 entered on November 3, 2020 at 12:02am

#1408. More Than One Shot
ID #997445 entered on November 2, 2020 at 12:01am

#1407. Happy Now?
ID #997330 entered on November 1, 2020 at 12:02am

#1406. More Tricks Than Treats
ID #997229 entered on October 31, 2020 at 4:04am

#1405. All The Long Years
ID #997135 entered on October 30, 2020 at 12:14am

#1404. But Mama, That's Where the Fun Is
ID #997051 entered on October 29, 2020 at 12:02am

#1403. Credit Where Credit Is Due
ID #996944 entered on October 28, 2020 at 12:10am

#1402. Time to Movie On
ID #996853 entered on October 27, 2020 at 12:05am

#1401. Such Stuff as Dreams Are Made On
ID #996764 entered on October 26, 2020 at 12:02am

#1400. Networking
ID #996685 entered on October 25, 2020 at 12:40am

#1399. Equations
ID #996595 entered on October 24, 2020 at 12:06am

#1398. I've Converted
ID #996521 entered on October 23, 2020 at 12:01am

#1397. Big Brother
ID #996443 entered on October 22, 2020 at 12:06am

#1396. Living the Dream
ID #996383 entered on October 21, 2020 at 12:01am

#1395. Predictions
ID #996298 entered on October 20, 2020 at 12:04am

#1394. Juxtaposition
ID #996208 entered on October 19, 2020 at 12:01am

#1393. Animal, Vegetable, Mineral
ID #996159 entered on October 18, 2020 at 12:02am

#1392. Catapostrophe
ID #996068 entered on October 17, 2020 at 12:00am

#1391. The Purge
ID #995975 entered on October 16, 2020 at 12:01am

#1390. Desert Ships
ID #995915 entered on October 15, 2020 at 12:02am

#1389. Morality Play
ID #995840 entered on October 14, 2020 at 12:06am

#1388. The Answer to the Ultimate Question
ID #995761 entered on October 13, 2020 at 12:01am

#1387. From the Ashes
ID #995688 entered on October 12, 2020 at 12:04am

#1386. If You Can't Stand the Heat...
ID #995608 entered on October 11, 2020 at 5:55am

#1385. Fail
ID #995512 entered on October 10, 2020 at 12:02am

#1384. The Pleasure Principle
ID #995429 entered on October 9, 2020 at 12:09am

#1383. Universal
ID #995330 entered on October 8, 2020 at 12:03am

#1382. Urine Good Hands
ID #995230 entered on October 7, 2020 at 12:03am

#1381. Road Hazard
ID #995149 entered on October 6, 2020 at 12:03am

#1380. Zodiacal Light
ID #995069 entered on October 5, 2020 at 12:02am

#1379. My Land
ID #994992 entered on October 4, 2020 at 12:04am

#1378. That's Not Kosher!
ID #994891 entered on October 3, 2020 at 12:03am

#1377. Dark and Stormy
ID #994824 entered on October 2, 2020 at 12:02am

#1376. Wasted
ID #994739 entered on October 1, 2020 at 12:18am

#1375. When September Ends
ID #994640 entered on September 30, 2020 at 12:02am

#1374. En-listed
ID #994530 entered on September 29, 2020 at 12:01am

#1373. Baggage
ID #994431 entered on September 28, 2020 at 12:06am

#1372. Not So Prompt
ID #994334 entered on September 27, 2020 at 2:27am

#1371. O'zapft is!
ID #994223 entered on September 26, 2020 at 12:08am

#1370. Don't You Forget About Me
ID #994138 entered on September 25, 2020 at 12:53am

#1369. Ex-Spend-Able
ID #994053 entered on September 24, 2020 at 12:03am

#1368. The Equation of Spontaneity
ID #993982 entered on September 23, 2020 at 12:12am

#1367. Déjà Vu All Over Again
ID #993899 entered on September 22, 2020 at 12:02am

#1366. Out Of Control
ID #993819 entered on September 21, 2020 at 12:05am

#1365. Patterns
ID #993759 entered on September 20, 2020 at 12:02am

#1364. Avalanche
ID #993687 entered on September 19, 2020 at 12:03am

#1363. Is Time Ever Really Free? Are We?
ID #993619 entered on September 18, 2020 at 12:01am

#1362. Lessons
ID #993535 entered on September 17, 2020 at 12:02am

#1361. Pappy? Happy.
ID #993461 entered on September 16, 2020 at 12:20am

#1360. It's an Ill Wind
ID #993382 entered on September 15, 2020 at 12:20am

#1359. The Inner Fright
ID #993295 entered on September 14, 2020 at 12:03am

#1358. Infinite Diversity in Infinite Combinations
ID #993223 entered on September 13, 2020 at 12:50am

#1357. Drinking about Thinking
ID #993134 entered on September 12, 2020 at 12:13am

#1356. Per Ardua Ad Astra
ID #993024 entered on September 11, 2020 at 12:02am

#1355. The Sound of Silence
ID #992939 entered on September 10, 2020 at 12:26am

#1354. Future Imperfect
ID #992827 entered on September 9, 2020 at 12:02am

#1353. To Explore Strange New Worlds
ID #992731 entered on September 8, 2020 at 12:02am

#1352. You CAN Take It With You
ID #992611 entered on September 7, 2020 at 1:30am

#1351. I Drink and I Know Things
ID #992517 entered on September 6, 2020 at 12:31am

#1350. The Force Is Strong in This One
ID #992410 entered on September 5, 2020 at 12:07am

#1349. Once in a Blue Moon
ID #992321 entered on September 4, 2020 at 12:01am

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