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Thursday, Apr. 25, 2024

8:13pm 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 Udon Thani

about 17 hours ago
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

about 17 hours ago
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

about 17 hours ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

a day ago
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

#2478. Revisited: "Another Avocado Article"
ID #1056983 entered on October 8, 2023 at 9:05am

#2477. Autonomy
ID #1056913 entered on October 7, 2023 at 9:13am

#2476. Plum
ID #1056859 entered on October 6, 2023 at 8:45am

#2475. Recursion (n.) 1. see Recursion
ID #1056798 entered on October 5, 2023 at 10:15am

#2474. Emotional Breakdown
ID #1056735 entered on October 4, 2023 at 10:26am

#2473. Ruby
ID #1056661 entered on October 3, 2023 at 11:12am

#2472. Bad Influence
ID #1056555 entered on October 2, 2023 at 8:53am

#2471. Revisited: "1984"
ID #1056484 entered on October 1, 2023 at 9:04am

#2470. Plugging Out
ID #1056440 entered on September 30, 2023 at 10:48am

#2469. Ring World
ID #1056392 entered on September 29, 2023 at 11:19am

#2468. This Side of the Pond
ID #1056335 entered on September 28, 2023 at 10:04am

#2467. Lost in Time
ID #1056291 entered on September 27, 2023 at 10:19am

#2466. Poe Lease
ID #1056238 entered on September 26, 2023 at 10:34am

#2465. Gud Speling
ID #1056196 entered on September 25, 2023 at 11:35am

#2464. Revisited: "What's Good for the Propaganda"
ID #1056151 entered on September 24, 2023 at 10:20am

#2463. Crepuscular Musings
ID #1056105 entered on September 23, 2023 at 10:13am

#2462. Let's Visit Spook-ane
ID #1056063 entered on September 22, 2023 at 8:40am

#2461. Cold Reading
ID #1056034 entered on September 21, 2023 at 10:43am

#2460. Labor Saving... Not
ID #1055978 entered on September 20, 2023 at 8:36am

#2459. A Meaty Discussion
ID #1055945 entered on September 19, 2023 at 8:26am

#2458. Idol Speculation
ID #1055909 entered on September 18, 2023 at 10:32am

#2457. Revisited: "Another Saturday Night"
ID #1055859 entered on September 17, 2023 at 8:28am

#2456. Penny For Your Thoughts
ID #1055814 entered on September 16, 2023 at 8:01am

#2455. Going Bananas
ID #1055769 entered on September 15, 2023 at 10:11am

#2454. How To Lose Money
ID #1055730 entered on September 14, 2023 at 9:14am

#2453. Hammer and Advil
ID #1055696 entered on September 13, 2023 at 8:29am

#2452. Morning Star
ID #1055633 entered on September 12, 2023 at 9:35am

#2451. Hindsight
ID #1055576 entered on September 11, 2023 at 11:13am

#2450. Revisited: "Annoying Things"
ID #1055524 entered on September 10, 2023 at 9:13am

#2449. Simplifying the Complex
ID #1055469 entered on September 9, 2023 at 10:01am

#2448. It's All One, Dude
ID #1055360 entered on September 8, 2023 at 9:26am

#2447. Less Than Super
ID #1055294 entered on September 7, 2023 at 8:33am

#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

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