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Tuesday, Jul. 2, 2024

12:22pm 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:

tracker

about 3 hours ago
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!

a day ago
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.

Elisa: Middle Aged Stik

Jun 29, 2024 at 11:12am
In response to "It Ain't Wrong"

Ain’t apparently begins as amn’t, a contraction for am not, which you can still hear in Ireland and Scotland today

I mean, an abundant number of Scotch and Irish immigrants ended up in the American South, so this tracks.

While a lot of people consider ain’t improper, it’s a very regular and legitimate part of many forms of English, including in Black English (AAVE). Be mindful that judging someone’s use of ain’t as “wrong” can be a very socially loaded act, to say the least.

For some reason, this reminds of one of the reasons I stopped reading Ask A Manager. A bunch of people were getting real uppity about the use of the phrase "baby daddy". Unsurprisingly, many of these people appeared white. One Black person in the comments finally had enough and threw down with this remark:

"I gotta say, as a black woman it grates to have phrases that come out of AAVE be appropriated, assigned negative connotation (likely because they come from black culture), then discarded with prejudice. If you’re using the phrase to conjure up stereotypical imagery, I can get on board with putting an end to that. But there are plenty of people for whom baby daddy or baby mama are not pejorative at all, just descriptors of the relationship in their dialect, and correcting them to “Father of my child” is just another case of denigrating minority speech patterns and legitimate AAVE grammatical constructions and upholding “white is right” standards."

(For more context, check out this link

1 Like

🌕 HuntersMoon

Jun 28, 2024 at 10:54am
In response to "It Ain't Wrong"

Ain't you on a roll today...

3 Like

Adherennium Dr of Phoolishness

Jun 27, 2024 at 11:53am
In response to "Wave Rider"

Horrifying fact, I once painted a reproduction of the Hokusai wave on our bathroom wall. Eventually of course it was painted over, but I like to fantasise that in some distant future it will be archaeologically excavated and held up as an example of early cultural appropriation, (badly executed too.)

1 Like

Annette

Jun 26, 2024 at 8:16pm
In response to "The Oz Hypothesis"

The nekked wimmin look like something that I might have drawn in first grade.

1 Like

Aiva Raine

Jun 25, 2024 at 10:16pm
In response to "Can't Spell Success without Sucs"

Ok- this made me truly LOL- "sipping a gin and tonic made with low-paid laborer tears"

Thank you. Totally agree with the rest of your article.

Money doesn't solve all problems but it sure as hell eliminates many and makes it easier to go places or buy things that can create some happiness. IE- a property somewhere quiet and peaceful and a trailer with which to chill on said property.

Rich people are typically clueless assholes.

1 Like

Anni Pon

Jun 25, 2024 at 9:30am
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

2 Like

#2546. Exterior Deterior
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#2545. Almost Done
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#2544. One Thousand Four Hundred Sixty-One
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#2543. Words of Wisdom
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#2542. Revisited: "Cosmological Comedy"
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#2539. Passed
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#2537. I'll Pass
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#2536. Cracked
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#2535. Moving On West
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#2534. Revisited: "The Attempted Resurrection of Words"
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#2533. Travel Advice, Part 4
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#2532. Travel Advice, Part 3
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#2531. Travel Advice, Part 2
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#2530. Travel Advice, Part 1
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#2527. Revisited: "So Much Winning"
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#2526. I Might Have Overused the Word 'Doom'
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#2525. The Wave
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#2524. Who?
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#2521. Lucky Town
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#2520. Revisited: "On Merit"
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#2519. Big Mistakes
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#2518. The Way It Gose
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#2517. Beaujolais Nouveau Day
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#2516. Forgive Me, For I Have Zinned
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#2515. Cheesy Jokes
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#2514. Secrets Revealed
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#2512. Snack Time
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#2509. Harvey Wallbanger Day
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#2507. Worlds Enough
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#2506. Revisited: "60 More Years!"
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#2505. Brew-tality
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#2504. A Brief History of Aliens
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#2502. Shorter Hops
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#2501. Punctuated
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#2500. Martian Law
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#2499. Revisited: "Man"
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#2498. Hunter's Moon
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#2497. Carmine
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#2496. The Dark Side
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#2495. Is There Anything It Can't Do?
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#2494. Hunter
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#2493. Testing My Patience
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#2491. The Optimism Trap
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#2490. Navy
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#2489. Crappily Ever After
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#2488. Rock Music
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#2486. The Trouble with Quibbles
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#2485. Revisited: "Headline Questions Are Usually Answered 'No'"
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#2484. Quantum Mind Tricks
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#2483. Amethyst
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#2482. Weird Barbaric Idiot Geek Dicks
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#2481. The Old Tongue
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#2480. Chartreuse
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#2479. I Am The Law
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#2478. Revisited: "Another Avocado Article"
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#2477. Autonomy
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#2476. Plum
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#2475. Recursion (n.) 1. see Recursion
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#2474. Emotional Breakdown
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#2473. Ruby
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#2472. Bad Influence
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#2471. Revisited: "1984"
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#2470. Plugging Out
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#2469. Ring World
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#2468. This Side of the Pond
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#2467. Lost in Time
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#2466. Poe Lease
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#2465. Gud Speling
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#2464. Revisited: "What's Good for the Propaganda"
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#2463. Crepuscular Musings
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#2462. Let's Visit Spook-ane
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#2461. Cold Reading
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#2460. Labor Saving... Not
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#2459. A Meaty Discussion
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#2458. Idol Speculation
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#2457. Revisited: "Another Saturday Night"
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#2456. Penny For Your Thoughts
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#2455. Going Bananas
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#2454. How To Lose Money
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#2453. Hammer and Advil
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#2452. Morning Star
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#2451. Hindsight
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#2450. Revisited: "Annoying Things"
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#2449. Simplifying the Complex
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#2448. It's All One, Dude
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#2447. Less Than Super
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