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Sunday, Jul. 7, 2024

7:57am 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 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.

#1250. These Questions Three
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#1249. Amusing Musical Musings
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#1248. Celebrate
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#1247. Superpowers
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#1245. Weird
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#1243. Useful
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#1242. Mind Games
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#1241. The Bucket
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#1240. Cleaning Up
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#1239. Reverse Road Trip
ID #983761 entered on May 17, 2020 at 12:02am

#1238. Who Ya Gonna Call?
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#1237. Liver Let Live
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#1236. Man of Letters
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#1235. Dream Vacation
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#1234. Free Willy-Nilly
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#1232. Myth of Family
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#1231. Lies, Damned Lies, and Memories
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#1230. Value Judgments
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#1229. Crossing My Path
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#1226. Recipe for Disaster
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#1221. Vitamin?
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#1220. I Drink Therefore I Am
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#1219. Fearful Symmetry
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#1217. Expanded Consciousness
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#1214. Sit Back
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#1213. Framed
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#1212. You're FIREd
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#1211. Top Bunk
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#1210. Historical Badass
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#1208. Again with the Millions
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#1207. Reflections
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#1206. The Electric Slide
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#1205. The Truth is Out There
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#1204. A Certain Point of View
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#1203. All In A Dream
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#1202. Snake Oil
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#1201. Learning the Language
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#1200. Awkward
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#1199. National Beer Day
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#1198. Does Whatever A Spider Can
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#1197. Authentic
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#1196. Murder Villages
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#1195. Ya Think?
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#1194. All Wet
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#1193. April Fools
ID #979863 entered on April 1, 2020 at 12:12am

#1192. Vive la Révolution!
ID #979755 entered on March 31, 2020 at 12:14am

#1191. Cunning Linguists
ID #979659 entered on March 30, 2020 at 12:16am

#1190. Doesn't Really Satisfy
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#1188. Lone
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#1187. A Unique Perspective
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#1185. Wisdom of the Waltz
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#1182. 'Murica!
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#1181. The Friendly Skies
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#1180. Bulk Smash!
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#1179. Rage of Aquarius
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#1178. The Pursuit of Grumpiness
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#1177. Music of the Spheres
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#1172. If You Don't Mindful
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#1171. No Time to Diet
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#1170. The Truth About Cats And Dogs
ID #977570 entered on March 9, 2020 at 12:17am

#1169. Make Me One With Everything
ID #977509 entered on March 8, 2020 at 12:23pm

#1168. For A Reason
ID #977380 entered on March 7, 2020 at 12:45am

#1167. Psychology Today
ID #977269 entered on March 6, 2020 at 12:03am

#1166. Moonlighting
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#1165. Laziness is the Milkman
ID #977034 entered on March 4, 2020 at 12:20am

#1164. Breathe
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#1163. No Clause for Celebration
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#1162. It Doesn't Count
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#1161. D'accord!
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#1160. I Think Therefore I Think
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#1159. The Original Dark Side
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#1158. What Is Art?
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#1155. Getting It Write
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#1154. Mutually Insured Destruction
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#1153. Self-Control to Major Tom
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#1151. No Song Today
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