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Friday, May. 3, 2024

4:12am EDT

Members: 742

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Total Online: 1,523

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

about 17 hours ago
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

1 Like

Elisa the Bunny Stik

a day ago
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
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 Montana

Apr 25, 2024 at 3:09am
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 Montana

Apr 25, 2024 at 2:58am
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

Apr 24, 2024 at 4:26pm
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

#2685. Butt Of Course
ID #1070406 entered on May 2, 2024 at 11:19am

#2684. Discovery
ID #1070355 entered on May 1, 2024 at 7:51am

#2683. Mad as Hell
ID #1070196 entered on April 30, 2024 at 9:51am

#2682. Supplementary
ID #1070095 entered on April 29, 2024 at 9:25am

#2681. Revisited: "Exercise"
ID #1069997 entered on April 28, 2024 at 10:25am

#2680. Pleasure and Pain
ID #1069877 entered on April 27, 2024 at 10:14am

#2679. On Track
ID #1069815 entered on April 26, 2024 at 3:55pm

#2678. Reality Cubed
ID #1069630 entered on April 25, 2024 at 2:18am

#2677. Tipped Out
ID #1069547 entered on April 24, 2024 at 1:02am

#2676. Going to the Dogs
ID #1069487 entered on April 23, 2024 at 11:38am

#2675. Hope for Hops
ID #1069370 entered on April 22, 2024 at 2:00am

#2674. Revisited: "Hack This"
ID #1069306 entered on April 21, 2024 at 9:17am

#2673. Macdonald's
ID #1069258 entered on April 20, 2024 at 11:45am

#2672. Mind the Menu
ID #1069178 entered on April 19, 2024 at 10:31am

#2671. Cash Stash
ID #1069054 entered on April 18, 2024 at 10:15am

#2670. Down Under
ID #1068972 entered on April 17, 2024 at 10:24am

#2669. What's the Difference Between a Duck?
ID #1068893 entered on April 16, 2024 at 10:19am

#2668. That's Cole
ID #1068809 entered on April 15, 2024 at 8:25am

#2667. Revisited: "Getting the Lead Out"
ID #1068727 entered on April 14, 2024 at 7:19am

#2666. Mawwiage...
ID #1068648 entered on April 13, 2024 at 2:25am

#2665. Coincidences
ID #1068587 entered on April 12, 2024 at 11:00am

#2664. Things Go Better With Cahokia
ID #1068505 entered on April 11, 2024 at 10:38am

#2663. A Cinderella Story
ID #1068434 entered on April 10, 2024 at 11:36am

#2662. Dark Side of the Moon
ID #1068297 entered on April 9, 2024 at 6:24pm

#2661. Louisville Sluggard
ID #1067994 entered on April 8, 2024 at 7:01am

#2660. Revisited: "Social Greases"
ID #1067846 entered on April 7, 2024 at 12:57am

#2659. Ageless
ID #1067789 entered on April 6, 2024 at 10:09am

#2658. Plurality
ID #1067635 entered on April 5, 2024 at 8:11am

#2657. It Ain't Nothin'
ID #1067553 entered on April 4, 2024 at 11:15am

#2656. Sumer in the City
ID #1067483 entered on April 3, 2024 at 9:25am

#2655. Sandpeople
ID #1067394 entered on April 2, 2024 at 10:56am

#2654. Easy to Get Fooled
ID #1067311 entered on April 1, 2024 at 12:17pm

#2653. Revisited: "Heartbreak"
ID #1067220 entered on March 31, 2024 at 8:32am

#2652. Dis or Dat Information
ID #1067184 entered on March 30, 2024 at 11:07am

#2651. From Sea To Mining Sea
ID #1067128 entered on March 29, 2024 at 9:27am

#2650. What're Y'all Doin'?
ID #1067075 entered on March 28, 2024 at 9:35am

#2649. Celestial Spheres
ID #1067027 entered on March 27, 2024 at 11:05am

#2648. Do What You Quill
ID #1066957 entered on March 26, 2024 at 9:09am

#2647. Served with Flare
ID #1066890 entered on March 25, 2024 at 8:50am

#2646. Revisited: "Took the train down to Athens"
ID #1066834 entered on March 24, 2024 at 8:15am

#2645. Montserrat
ID #1066768 entered on March 23, 2024 at 10:24am

#2644. Trope-Osphere
ID #1066720 entered on March 22, 2024 at 10:33am

#2643. Socra-Tease
ID #1066678 entered on March 21, 2024 at 10:06am

#2642. Not My Baili-Wiki
ID #1066614 entered on March 20, 2024 at 10:30am

#2641. Stardust
ID #1066562 entered on March 19, 2024 at 9:18am

#2640. Cookie Wars
ID #1066490 entered on March 18, 2024 at 9:36am

#2639. Revisited: "Power"
ID #1066413 entered on March 17, 2024 at 9:27am

#2638. Substandard
ID #1066354 entered on March 16, 2024 at 10:52am

#2637. Why So Selfies?
ID #1066306 entered on March 15, 2024 at 9:38am

#2636. Current Events
ID #1066257 entered on March 14, 2024 at 9:54am

#2635. It's "Desert" Not "Dessert"
ID #1066209 entered on March 13, 2024 at 10:52am

#2634. Mind Matters
ID #1066147 entered on March 12, 2024 at 9:26am

#2633. Cheeses Crisis
ID #1066054 entered on March 11, 2024 at 8:26am

#2632. Revisited: "Links are Back!"
ID #1065994 entered on March 10, 2024 at 9:59am

#2631. Daydream Believer
ID #1065919 entered on March 9, 2024 at 9:27am

#2630. Law and Ordering Alcohol
ID #1065851 entered on March 8, 2024 at 8:25am

#2629. Zoned Out
ID #1065784 entered on March 7, 2024 at 9:23am

#2628. Les Langues d'Amour
ID #1065695 entered on March 6, 2024 at 8:16am

#2627. Ignorance is...
ID #1065605 entered on March 5, 2024 at 11:12am

#2626. Facts Simile
ID #1065530 entered on March 4, 2024 at 9:03am

#2625. Revisited: "Sea What I Did There"
ID #1065466 entered on March 3, 2024 at 9:37am

#2624. Thought Bubble
ID #1065370 entered on March 2, 2024 at 6:33am

#2623. They Ain't Here
ID #1065309 entered on March 1, 2024 at 8:39am

#2622. Quantum Leap Day
ID #1065222 entered on February 29, 2024 at 7:46am

#2621. That Was Easy
ID #1065075 entered on February 28, 2024 at 8:49am

#2620. Olive It And More
ID #1064998 entered on February 27, 2024 at 11:32am

#2619. Round and Round
ID #1064910 entered on February 26, 2024 at 10:11am

#2618. Revisited: "Cheese? What Kind of Cheese? I Want Brie"
ID #1064849 entered on February 25, 2024 at 10:07am

#2617. Nerdy Words
ID #1064779 entered on February 24, 2024 at 10:04am

#2616. Coming Up the Pike
ID #1064737 entered on February 23, 2024 at 10:28am

#2615. Curiosity
ID #1064670 entered on February 22, 2024 at 8:54am

#2614. That's Not Life
ID #1064595 entered on February 21, 2024 at 9:33am

#2613. Dahlia Dreaming
ID #1064499 entered on February 20, 2024 at 10:48am

#2612. Hogsheads per Furlong
ID #1064442 entered on February 19, 2024 at 9:15am

#2611. Revisited: "Cat Stuff"
ID #1064378 entered on February 18, 2024 at 9:36am

#2610. Inside Voice
ID #1064327 entered on February 17, 2024 at 9:04am

#2609. Violet
ID #1064272 entered on February 16, 2024 at 9:54am

#2608. PIE in Your Face
ID #1064218 entered on February 15, 2024 at 10:28am

#2607. Other Stuff We Don't Know
ID #1064168 entered on February 14, 2024 at 10:18am

#2606. Lurk in the Woods
ID #1064118 entered on February 13, 2024 at 9:33am

#2605. Cancel Cancel
ID #1064055 entered on February 12, 2024 at 9:07am

#2604. Revisited: "So it Ends"
ID #1063975 entered on February 11, 2024 at 9:24am

#2603. The Abyss Stares Also
ID #1063912 entered on February 10, 2024 at 9:16am

#2602. Running Stitch
ID #1063834 entered on February 9, 2024 at 9:53am

#2601. Freeze Frame
ID #1063762 entered on February 8, 2024 at 11:05am

#2600. Pinchers
ID #1063694 entered on February 7, 2024 at 10:47am

#2599. Stocking
ID #1063630 entered on February 6, 2024 at 9:47am

#2598. The Streak
ID #1063550 entered on February 5, 2024 at 10:48am

#2597. Revisited: "Poker"
ID #1063436 entered on February 4, 2024 at 9:04am

#2596. Burgundy
ID #1063374 entered on February 3, 2024 at 10:38am

#2595. Rats!
ID #1063315 entered on February 2, 2024 at 9:48am

#2594. And It Was All Yellow
ID #1063273 entered on February 1, 2024 at 11:19am

#2593. Mixed-Up
ID #1063230 entered on January 31, 2024 at 10:04am

#2592. Koalemos
ID #1063180 entered on January 30, 2024 at 11:00am

#2591. Ice Sea Moons
ID #1063143 entered on January 29, 2024 at 11:13am

#2590. Revisited: "Who"
ID #1063091 entered on January 28, 2024 at 9:27am

#2589. Spaced Out
ID #1063046 entered on January 27, 2024 at 10:40am

#2588. Today is Satireday
ID #1062993 entered on January 26, 2024 at 10:22am

#2587. Appropriate
ID #1062941 entered on January 25, 2024 at 8:36am

#2586. Pronouncements
ID #1062909 entered on January 24, 2024 at 12:40pm

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