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Friday, Apr. 19, 2024

11:19pm 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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10 Most Recent Blog Comments:

Elisa the Bunny Stik

about 11 hours ago
In response to "Mind the Menu"

"Maybe I'm in the minority here, but I assert there's nothing inherently wrong with nostalgia."

Given the rise of restorative nostalgia, I'm inclined to disagree (and yes, I think this distinction is necessary).

https://www.psychologytoday.com/us/blog/time-travelling-apollo/201606/the-t wo-faces-nostalgia

1 Like

Aennaytte: Free & Wild in GoT

about 11 hours ago
In response to "Mind the Menu"

Not to mention that Two Buck Chuck is now Three Fifty Chuck.

2 Like

Wordsmitty ✍️

Apr 17, 2024 at 7:13pm
In response to "Down Under"

Water? What about where their sewage waste goes?

1 Like

Elycia Lee ☮

Apr 16, 2024 at 10:43am
In response to "What's the Difference Between a Duck?"

So happy that there is an answer to that Alice in the Wonderland riddle.

Finally. Fascinating stuff. All of them. There is something rather philosophical about comedy. You are certainly right there.

Elisa the Bunny Stik

Apr 15, 2024 at 8:35am
In response to "That's Cole"

"I don't know what the latest fad food is, but I can almost guarantee that behind the fad is someone with money trying to make more of it."

I'd say there are multiple fad foods, including goji berries. That said, cauliflower became trendy in 2018 and has maintained some level of staying power. I still see cauliflower rice as an option in many places across the US.

4 Like

Elisa the Bunny Stik

Apr 13, 2024 at 6:10am
In response to "Mawwiage..."

"Or, at the very least, it's an emotional bond more than a business arrangement."

And for a substantial subset of parents, it's neither. They either just want kids to show off like trophies or dive headfirst into various forms of abuse.

3 Like

Aennaytte: Free & Wild in GoT

Apr 12, 2024 at 12:39pm
In response to "Coincidences"

Some words even cross species.

My golden cat calls me Mom frequently.

1 Like

tj ~ endeavors to persevere!

Apr 11, 2024 at 1:58pm
In response to "A Cinderella Story"

Do you mean something like Carl having to work in the garage for his wicked step-dad while his brothers party? He was polishing an old hubcap that was magical and the next thing he meets a rich cougar at the club but has to leave by midnight when the spell wears off. As he exits he looses a boot. The cougar takes the boot with her and ends up having car problems the following day and stops at the garage where she notices Carl sweeping the floor with only one boot. She hands him the boot, it fits, and they are last seen sailing off on her yacht.

1 Like

tj ~ endeavors to persevere!

Apr 11, 2024 at 1:48pm
In response to "Things Go Better With Cahokia"

I bet they left because there wasn't anymore deer to barbecue.

2 Like

Robert Waltz

Apr 10, 2024 at 11:05am
In response to "Dark Side of the Moon"

⭐️Jellyfish⭐️

: Also known as a swag bag, but I usually prefer alliteration to rhyme (and also, since I pretend to be a writer, I like coming up with my own terms). No idea what you call them on that side of the pond. It's not technically "bling" because there wasn't any personal decoration, but it had things like certified sun-gazer glasses, a copy of their special eclipse bottle label art, a winery-logo corkscrew, and some delicious truffles (the chocolate kind, not the mushroom kind). Kind of like a Christmas stocking, but in April and for wine and astronomy nerds.

#2272. Eight Isn't Enough
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#2271. Stupid Answer
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#2270. Word Origins
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#2269. Begging, the Question
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#2268. Revisited: "WTC"
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#2267. Cache Is King
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#2266. Musk I?
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#2265. Saison de Cueillette
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#2264. Behave
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#2263. Umami
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#2261. Revisited: "Sniff"
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#2259. Tough
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#2258. Null and Void
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#2257. Purrfectly Dark
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#2256. In Your Face
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#2255. What You Will
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#2254. Revisited: "Random Thoughts"
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#2249. The Cure
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#2248. Remember What Now?
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#2247. Revisited: "No Links"
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#2246. What the Bike?
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#2241. When Not In Rome
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#2238. Car Care
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#2237. Origin Stories
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#2236. Watch It Wiggle
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#2235. Pareidolia
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#2234. The Building Code
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#2233. Revisited: "Lassie"
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#2232. Turning Over a New Leaf
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#2231. Rants At A Picnic
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#2230. A Star is Born
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#2229. Like the Plague
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#2228. In The Beginning Was the Emoji
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#2227. Psych Ops
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#2224. Bizspeak
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#2223. Monopoly
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#2222. Satan's Earwax
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#2221. AI See What You Did There
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#2220. Minerals... From Spaaaaaaaace
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#2219. Revisited: "Scare Tactics"
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#2218. Thinking Inside the Box
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#2216. Read All the Books
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#2215. Survivalism
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#2210. Kitchen Bitchin'
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#2209. Librarians
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#2208. Revisited: "Eruv L'olam"
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#2207. Naturally
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#2205. Greetings from Asbury Park, NJ
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#2204. Yeast River
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#2203. Imbalance
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#2202. Tipping Point
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#2201. Mushroom Mushroom
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#2200. Wake Up Call
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#2199. Born to Forget
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#2198. Revisited: "Someone's Birthday"
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#2197. Syne of the Times
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#2196. Playing Chicken
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#2195. Consumer
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#2194. Triskaidekaphobia
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#2193. Origins
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#2192. Symbiosis
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#2191. Revisited: "NaNo?"
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#2190. Reason for the Sneezin'
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#2189. Mad World
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#2188. It's Trying to Kill You
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#2187. Elves: A Field Guide
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#2186. Preservation
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#2185. Soup Chef
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#2184. Revisited: "The Only Certainty is Uncertainty"
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#2183. Facts Machine
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#2182. Not Giving Up the Ghost
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#2181. Luck You Too
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#2180. Not Buying It
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#2179. Three Years
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#2178. Colony
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#2177. Revisited: "Deep Dive"
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#2176. You Mean Like From The Toilet?
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#2175. Kanterpoint
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#2174. Think Tanked
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#2173. It's Not Even Half Full
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