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Sunday, Jul. 7, 2024

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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 Montana

about 20 hours ago
In response to "Down in the Valley"

I would like to get to the Loire. There's plenty to see so I'd just take it slow, a saunter instead of a march, a Rêverie (think Debussy).

There's quite a lot on youtube but I don't have time to get lost today.

When you are there... get lost.

1 Like

Kåre Enga in Montana

a day ago
In response to "It's Called 'Fiction' For a Reason"

For us older folks, Sweet Child*, "Leave it to Beaver" was the ideal... unfortunately, that ideal existed for very few people. And for many it was never their "American Dream".

*anyone younger than me is a 'child'.

Wordsmitty ✍️

a day ago
In response to "It's Called 'Fiction' For a Reason"

"cars inevitably explode when run off cliffs." Has anyone seen the "Myth Busters" episode of running cars off cliff to see if they explode? Well, there's your answer.

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "It's Called 'Fiction' For a Reason"

"in the alternate universe of The Watchmen (the original graphic novel, published in the late 80s), the President was Robert Redford."

Given Redford's politics, some people might consider this a utopia.

"Anyway, it's no surprise that NASA got its idea from German cinema instead of French, considering the history of NASA."

I will not make remarks about Air France's safety record. I will not make remarks about Air France's safety record. I will not make remarks about Air France's safety record.

2 Like

tj ~ endeavors to persevere!

a day ago
In response to "It's Called 'Fiction' For a Reason"

Great post. It seems now it's not ideas from movies as much as, "I seen it on YouTube, so it must be true", or at least that's been my observation.

2 Like

🌕 HuntersMoon

Jul 3, 2024 at 10:12am
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.

#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

#1348. Everyone's a Critic
ID #992214 entered on September 3, 2020 at 12:07am

#1347. Mission: Difficult
ID #992094 entered on September 2, 2020 at 12:01am

#1346. Cheese? What Kind of Cheese? I Want Brie
ID #992001 entered on September 1, 2020 at 12:08am

#1345. Another Month in the Past
ID #991928 entered on August 31, 2020 at 12:01am

#1344. Nothing Matters
ID #991852 entered on August 30, 2020 at 12:50am

#1343. Rare Earth
ID #991792 entered on August 29, 2020 at 12:03am

#1342. Good? Evil? A Jedi Cares Not For These Things
ID #991729 entered on August 28, 2020 at 12:07am

#1341. No, It's Not 36.
ID #991669 entered on August 27, 2020 at 12:12am

#1340. For the Rest of It
ID #991593 entered on August 26, 2020 at 12:02am

#1339. Wave Function Collapse
ID #991528 entered on August 25, 2020 at 12:06am

#1338. Orange You Glad This Wasn't You?
ID #991450 entered on August 24, 2020 at 12:04am

#1337. Fur the Fun of It
ID #991386 entered on August 23, 2020 at 12:02am

#1336. Just the Tip
ID #991324 entered on August 22, 2020 at 12:06am

#1335. Quantum Speculation
ID #991258 entered on August 21, 2020 at 12:05am

#1334. Good Willpower Hunting
ID #991199 entered on August 20, 2020 at 12:18am

#1333. Mind Map
ID #991137 entered on August 19, 2020 at 12:10am

#1332. As the Turn Worlds (or whatever)
ID #991071 entered on August 18, 2020 at 12:02am

#1331. The Real You
ID #990991 entered on August 17, 2020 at 12:08am

#1330. Changes in Attitude
ID #990910 entered on August 16, 2020 at 12:04am

#1329. Wait, Isn't Oxygen A GOOD Thing?
ID #990810 entered on August 15, 2020 at 12:08am

#1328. Go Home, Evolution. You're Drunk.
ID #990710 entered on August 14, 2020 at 12:01am

#1327. On Merit
ID #990638 entered on August 13, 2020 at 12:06am

#1326. I Got a Rock
ID #990565 entered on August 12, 2020 at 12:02am

#1325. Once More With Feeling
ID #990492 entered on August 11, 2020 at 12:20am

#1324. The The
ID #990401 entered on August 10, 2020 at 12:03am

#1323. Wine, Cheese, and Bread
ID #990304 entered on August 9, 2020 at 12:07am

#1322. The Great Gig in the Sky
ID #990216 entered on August 8, 2020 at 12:01am

#1321. Lox Pie
ID #990157 entered on August 7, 2020 at 12:02am

#1320. Panpsychoticism
ID #990052 entered on August 6, 2020 at 12:03am

#1319. Only the (not so) Lonely
ID #989926 entered on August 5, 2020 at 12:11am

#1318. Decisions, Decisions
ID #989830 entered on August 4, 2020 at 12:02am

#1317. Dueling Scientists
ID #989758 entered on August 3, 2020 at 12:05am

#1316. Eruv L'olam
ID #989699 entered on August 2, 2020 at 12:26am

#1315. Remember, Remember
ID #989626 entered on August 1, 2020 at 12:02am

#1314. Where Jokes Go to Die
ID #989563 entered on July 31, 2020 at 12:01am

#1313. Thoughts for Thirty
ID #989487 entered on July 30, 2020 at 12:21am

#1312. Humanity's Last Invention
ID #989410 entered on July 29, 2020 at 12:01am

#1311. Something is Rotten in Belgium
ID #989336 entered on July 28, 2020 at 12:21am

#1310. The Not-Shining
ID #989226 entered on July 27, 2020 at 12:02am

#1309. One True Pizza
ID #989146 entered on July 26, 2020 at 12:11am

#1308. Week
ID #989070 entered on July 25, 2020 at 12:03am

#1307. Freaky
ID #989000 entered on July 24, 2020 at 12:11am

#1306. Butcher
ID #988913 entered on July 23, 2020 at 12:02am

#1305. Vice-Virtue
ID #988828 entered on July 22, 2020 at 12:02am

#1304. Dear Me
ID #988737 entered on July 21, 2020 at 12:05am

#1303. Man on the Moon
ID #988635 entered on July 20, 2020 at 12:01am

#1302. Solitaire
ID #988560 entered on July 19, 2020 at 4:04am

#1301. Gnaw Bone
ID #988445 entered on July 18, 2020 at 12:06am

#1300. Driver's Seat
ID #988362 entered on July 17, 2020 at 12:01am

#1299. Comet Sutra
ID #988287 entered on July 16, 2020 at 12:18am

#1298. The Pun is Mightier than the Sword
ID #988201 entered on July 15, 2020 at 12:22am

#1297. It's a Trappist!
ID #988106 entered on July 14, 2020 at 12:17am

#1296. Summer Ale
ID #988003 entered on July 13, 2020 at 12:01am

#1295. Blog Standard
ID #987883 entered on July 12, 2020 at 12:01am

#1294. Sounding the Alarm
ID #987788 entered on July 11, 2020 at 12:01am

#1293. Catfall
ID #987703 entered on July 10, 2020 at 12:01am

#1292. That's Nice
ID #987614 entered on July 9, 2020 at 12:01am

#1291. All On That Day
ID #987524 entered on July 8, 2020 at 12:11am

#1290. You're My Inspiration
ID #987434 entered on July 7, 2020 at 12:12am

#1289. The Edge of the World
ID #987334 entered on July 6, 2020 at 11:42am

#1288. Inspiration and Aspiration
ID #987254 entered on July 5, 2020 at 12:23am

#1287. Forty
ID #987175 entered on July 4, 2020 at 12:14am

#1286. Hallelujah
ID #987097 entered on July 3, 2020 at 12:05am

#1285. East is West
ID #987000 entered on July 2, 2020 at 10:44am

#1284. Prenatal Parental
ID #986895 entered on July 1, 2020 at 12:01am

#1283. Ritual
ID #986814 entered on June 30, 2020 at 12:23am

#1282. Words Enough, And Time
ID #986742 entered on June 29, 2020 at 12:02am

#1281. Protein or Amateurtein?
ID #986685 entered on June 28, 2020 at 7:19am

#1280. Something about Nothing
ID #986616 entered on June 27, 2020 at 12:07am

#1279. Under Pressure
ID #986550 entered on June 26, 2020 at 12:14am

#1278. Sense of Wonder
ID #986466 entered on June 25, 2020 at 12:30am

#1277. Anthem
ID #986394 entered on June 24, 2020 at 12:03am

#1276. Flippers
ID #986319 entered on June 23, 2020 at 12:31am

#1275. The Candyman Can
ID #986175 entered on June 22, 2020 at 12:29am

#1274. Business
ID #986107 entered on June 21, 2020 at 12:10am

#1273. Omen
ID #986037 entered on June 20, 2020 at 12:17am

#1272. Watch
ID #985962 entered on June 19, 2020 at 12:23am

#1271. Great Scots
ID #985893 entered on June 18, 2020 at 12:14am

#1270. Zombie
ID #985822 entered on June 17, 2020 at 12:08am

#1269. Fat Chance
ID #985751 entered on June 16, 2020 at 12:22am

#1268. Meat the Press
ID #985674 entered on June 15, 2020 at 12:16am

#1267. Oh, Pinions
ID #985608 entered on June 14, 2020 at 12:16am

#1266. Shoot for the Moon
ID #985561 entered on June 13, 2020 at 12:55am

#1265. Future Tense
ID #985508 entered on June 12, 2020 at 12:24am

#1264. I'm Not Saying It's Aliens
ID #985430 entered on June 11, 2020 at 12:04am

#1263. Sweet Emotion
ID #985370 entered on June 10, 2020 at 12:30am

#1262. Blame it on the Rain
ID #985316 entered on June 9, 2020 at 12:21am

#1261. Intractable Language
ID #985224 entered on June 8, 2020 at 12:24am

#1260. Consumer Revolt
ID #985145 entered on June 7, 2020 at 12:26am

#1259. Save
ID #985086 entered on June 6, 2020 at 12:17am

#1258. Oh Behave
ID #985027 entered on June 5, 2020 at 12:01am

#1257. Building Around
ID #984955 entered on June 4, 2020 at 12:40am

#1256. Fun, Fun, Fun
ID #984895 entered on June 3, 2020 at 12:44am

#1255. Twelve Faces
ID #984825 entered on June 2, 2020 at 1:08am

#1254. Monster
ID #984737 entered on June 1, 2020 at 12:17am

#1253. Draggin'
ID #984650 entered on May 31, 2020 at 12:18am

#1252. The End -- but not really
ID #984601 entered on May 30, 2020 at 12:27am

#1251. Dream Home
ID #984523 entered on May 29, 2020 at 12:08am

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