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Thursday, Jul. 4, 2024

3:03pm 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:

🌕 HuntersMoon

a day ago
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.

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

#1648. Somewhere in Minnesota
ID #1012759 entered on June 30, 2021 at 12:07am

#1647. The Forbidden Door
ID #1012703 entered on June 29, 2021 at 1:23am

#1646. Bloomington
ID #1012648 entered on June 28, 2021 at 6:35am

#1645. Athens
ID #1012591 entered on June 27, 2021 at 1:17am

#1644. Spel Chek
ID #1012535 entered on June 26, 2021 at 12:02am

#1643. Outstanding
ID #1012488 entered on June 25, 2021 at 12:03am

#1642. No Accounting for Taste
ID #1012432 entered on June 24, 2021 at 12:02am

#1641. Dream a Little Dream
ID #1012373 entered on June 23, 2021 at 12:01am

#1640. Imperial Decree
ID #1012324 entered on June 22, 2021 at 12:02am

#1639. Count Me In
ID #1012247 entered on June 21, 2021 at 12:13am

#1638. Plans
ID #1012194 entered on June 20, 2021 at 12:01am

#1637. Pompeii Attention Now
ID #1012126 entered on June 19, 2021 at 12:03am

#1636. Superman
ID #1012072 entered on June 18, 2021 at 12:08am

#1635. Souperman
ID #1011997 entered on June 17, 2021 at 12:04am

#1634. Singing Neutrinos
ID #1011947 entered on June 16, 2021 at 12:06am

#1633. I Expected This
ID #1011896 entered on June 15, 2021 at 12:02am

#1632. Dunning-Kruger-Rand
ID #1011839 entered on June 14, 2021 at 12:02am

#1631. The One True Rule
ID #1011779 entered on June 13, 2021 at 2:27am

#1630. Inevitable
ID #1011710 entered on June 12, 2021 at 12:02am

#1629. Useful
ID #1011656 entered on June 11, 2021 at 12:03am

#1628. Lazy-er Light
ID #1011579 entered on June 10, 2021 at 12:03am

#1627. Language Barrier
ID #1011528 entered on June 9, 2021 at 12:07am

#1626. Out of the Valley
ID #1011473 entered on June 8, 2021 at 12:01am

#1625. I Don't Have Time for This
ID #1011420 entered on June 7, 2021 at 12:02am

#1624. Fun & Games
ID #1011375 entered on June 6, 2021 at 12:12am

#1623. Random Access Memory
ID #1011329 entered on June 5, 2021 at 12:01am

#1622. Unproven
ID #1011269 entered on June 4, 2021 at 12:27am

#1621. Paper or Plastic?
ID #1011209 entered on June 3, 2021 at 12:02am

#1620. Survivor
ID #1011143 entered on June 2, 2021 at 12:04am

#1619. Kids These Days
ID #1011075 entered on June 1, 2021 at 12:02am

#1618. Memorial
ID #1011036 entered on May 31, 2021 at 12:02am

#1617. Moving Right Along
ID #1010983 entered on May 30, 2021 at 12:03am

#1616. Promptly
ID #1010947 entered on May 29, 2021 at 12:18am

#1615. Fail
ID #1010894 entered on May 28, 2021 at 12:02am

#1614. And The First Shall Be Last
ID #1010837 entered on May 27, 2021 at 12:03am

#1613. Planet Plan-It
ID #1010781 entered on May 26, 2021 at 12:39am

#1612. Big Dummy
ID #1010726 entered on May 25, 2021 at 10:10am

#1611. On with the Show
ID #1010635 entered on May 24, 2021 at 12:17am

#1610. By Any Other Name
ID #1010590 entered on May 23, 2021 at 12:03am

#1609. A Challenge
ID #1010546 entered on May 22, 2021 at 12:02am

#1608. Cheeses Crust
ID #1010505 entered on May 21, 2021 at 12:01am

#1607. Unalienable
ID #1010459 entered on May 20, 2021 at 12:05am

#1606. Adventure
ID #1010404 entered on May 19, 2021 at 10:56am

#1605. Screening
ID #1010351 entered on May 18, 2021 at 10:55am

#1604. Connections
ID #1010284 entered on May 17, 2021 at 9:22am

#1603. For Better or Worse
ID #1010240 entered on May 16, 2021 at 12:04am

#1602. In a Red Hood
ID #1010195 entered on May 15, 2021 at 12:41am

#1601. Universal Plot
ID #1010154 entered on May 14, 2021 at 10:23am

#1600. Wonderlust
ID #1010087 entered on May 13, 2021 at 12:01am

#1599. No Time to Morn
ID #1010041 entered on May 12, 2021 at 12:02am

#1598. Cool Fusion
ID #1009998 entered on May 11, 2021 at 12:01am

#1597. Some Mother Time
ID #1009954 entered on May 10, 2021 at 4:40pm

#1596. La Langue
ID #1009897 entered on May 9, 2021 at 12:05am

#1595. Naturally
ID #1009846 entered on May 8, 2021 at 12:02am

#1594. Dream Reaver
ID #1009802 entered on May 7, 2021 at 12:03am

#1593. Never Volunteer
ID #1009737 entered on May 6, 2021 at 12:20am

#1592. Taking Off
ID #1009675 entered on May 5, 2021 at 12:02am

#1591. A Day
ID #1009628 entered on May 4, 2021 at 10:20am

#1590. Getting Salty
ID #1009557 entered on May 3, 2021 at 12:01am

#1589. Making Sense of It All
ID #1009516 entered on May 2, 2021 at 12:02am

#1588. Liberating the Angel
ID #1009449 entered on May 1, 2021 at 12:03am

#1587. Conscious Decisions
ID #1009392 entered on April 30, 2021 at 7:28am

#1586. Hammer Time
ID #1009331 entered on April 29, 2021 at 12:03am

#1585. Competition
ID #1009252 entered on April 28, 2021 at 12:15am

#1584. Creating without a Creator
ID #1009201 entered on April 27, 2021 at 12:02am

#1583. That's Write
ID #1009149 entered on April 26, 2021 at 12:01am

#1582. Secret
ID #1009082 entered on April 25, 2021 at 12:04am

#1581. Open Up
ID #1009033 entered on April 24, 2021 at 12:13am

#1580. As If It Happened Only Yesterday
ID #1008989 entered on April 23, 2021 at 12:01am

#1579. I Don't Buy It
ID #1008945 entered on April 22, 2021 at 12:02am

#1578. Mind Matters
ID #1008886 entered on April 21, 2021 at 12:07am

#1577. Real Men of Genius
ID #1008815 entered on April 20, 2021 at 12:03am

#1576. Just the Tip
ID #1008753 entered on April 19, 2021 at 12:01am

#1575. Just the Facts
ID #1008685 entered on April 18, 2021 at 12:01am

#1574. State Hate
ID #1008644 entered on April 17, 2021 at 12:02am

#1573. Healthy, Wealthy, and Wise
ID #1008600 entered on April 16, 2021 at 12:03am

#1572. Fringe
ID #1008535 entered on April 15, 2021 at 12:52am

#1571. Wagging Tales
ID #1008482 entered on April 14, 2021 at 12:02am

#1570. Ancient Life
ID #1008426 entered on April 13, 2021 at 12:05am

#1569. Head in the Clouds
ID #1008370 entered on April 12, 2021 at 12:01am

#1568. Brain Trust
ID #1008209 entered on April 11, 2021 at 12:01am

#1567. One Weird Trick
ID #1008142 entered on April 10, 2021 at 12:05am

#1566. There's a Blaze of Light in Every Word
ID #1008074 entered on April 9, 2021 at 12:02am

#1565. Not-Reading List
ID #1008003 entered on April 8, 2021 at 12:03am

#1564. Ain't Goin' Nowhere
ID #1007916 entered on April 7, 2021 at 12:04am

#1563. You Call That Easy?
ID #1007848 entered on April 6, 2021 at 12:02am

#1562. Procrasti-later
ID #1007766 entered on April 5, 2021 at 12:01am

#1561. Past Intense
ID #1007712 entered on April 4, 2021 at 12:01am

#1560. Word Says What
ID #1007638 entered on April 3, 2021 at 12:01am

#1559. Scout Chip
ID #1007556 entered on April 2, 2021 at 12:02am

#1558. No Fooling
ID #1007417 entered on April 1, 2021 at 12:02am

#1557. The Cure
ID #1007361 entered on March 31, 2021 at 12:02am

#1556. Lawn Order
ID #1007295 entered on March 30, 2021 at 12:01am

#1555. Totally Not Financial Advice
ID #1007228 entered on March 29, 2021 at 12:01am

#1554. Facts... Maybe?
ID #1007169 entered on March 28, 2021 at 12:03am

#1553. Alone at Low Interest
ID #1007113 entered on March 27, 2021 at 12:03am

#1552. Dream Territory
ID #1007070 entered on March 26, 2021 at 12:02am

#1551. Certain Things
ID #1007019 entered on March 25, 2021 at 12:01am

#1550. What's a Wonk?
ID #1006963 entered on March 24, 2021 at 12:01am

#1549. Denial is More than Just a River in Egypt
ID #1006902 entered on March 23, 2021 at 12:08am

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