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Saturday, May. 18, 2024

12:30am 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:

Aiva Raine

about 6 hours ago
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

#900. Weighty Matters
ID #960028 entered on June 2, 2019 at 12:10am

#899. On the Bias
ID #959965 entered on June 1, 2019 at 12:49am

#898. The Magic that Actually Works
ID #959930 entered on May 31, 2019 at 12:20am

#897. Parting Shot
ID #959858 entered on May 30, 2019 at 12:17am

#896. My Canny Vice
ID #959811 entered on May 29, 2019 at 1:19am

#895. On Being Wrong
ID #959762 entered on May 28, 2019 at 12:47am

#894. Memorial
ID #959695 entered on May 27, 2019 at 12:12am

#893. Save Game
ID #959630 entered on May 26, 2019 at 12:22am

#892. Weekend
ID #959575 entered on May 25, 2019 at 12:13am

#891. Self-Control
ID #959523 entered on May 24, 2019 at 12:01am

#890. Book Learnin'
ID #959477 entered on May 23, 2019 at 12:27am

#889. Rocket Surgeon
ID #959422 entered on May 22, 2019 at 12:19am

#888. The Derivative of Opinion
ID #959365 entered on May 21, 2019 at 12:42am

#887. Cycles
ID #959306 entered on May 20, 2019 at 12:15am

#886. Idealized
ID #959246 entered on May 19, 2019 at 12:23am

#885. The Only Thing I Do Every Day
ID #959174 entered on May 18, 2019 at 12:05am

#884. Life Sucks And Then You Die
ID #959121 entered on May 17, 2019 at 12:29am

#883. Mid-May Messages
ID #959073 entered on May 16, 2019 at 12:29am

#882. It's About Time
ID #958987 entered on May 15, 2019 at 12:17am

#881. Burned Out
ID #958910 entered on May 14, 2019 at 12:57am

#880. Just Right
ID #958848 entered on May 13, 2019 at 12:13am

#879. Human Nurture
ID #958785 entered on May 12, 2019 at 12:14am

#878. The Gift
ID #958735 entered on May 11, 2019 at 12:29am

#877. Someone's Birthday
ID #958652 entered on May 10, 2019 at 12:47am

#876. Far from Home
ID #958596 entered on May 9, 2019 at 1:18am

#875. In Space, No One Can Watch You Drink
ID #958501 entered on May 8, 2019 at 12:08am

#874. Subjective Impressions
ID #958436 entered on May 7, 2019 at 12:30am

#873. Room for Improvement
ID #958308 entered on May 6, 2019 at 12:16am

#872. Nothing Really Sucks
ID #958246 entered on May 5, 2019 at 12:07am

#871. Exploring the Unknown
ID #958202 entered on May 4, 2019 at 12:18am

#870. Heritage
ID #958116 entered on May 3, 2019 at 12:45am

#869. The Lamp
ID #958035 entered on May 2, 2019 at 12:59am

#868. Mayday
ID #957959 entered on May 1, 2019 at 12:23am

#867. Vacation
ID #956598 entered on April 15, 2019 at 1:17am

#866. Time to Change
ID #955484 entered on April 1, 2019 at 12:14am

#865. Bender
ID #954926 entered on March 25, 2019 at 3:02am

#864. Depressing
ID #954673 entered on March 21, 2019 at 12:47am

#863. Balance
ID #954627 entered on March 20, 2019 at 12:47am

#862. Good and Gooder
ID #954570 entered on March 19, 2019 at 1:16am

#861. Duck!
ID #954359 entered on March 15, 2019 at 11:58am

#860. Pi Day
ID #954305 entered on March 14, 2019 at 12:01am

#859. No Music in Me
ID #954251 entered on March 13, 2019 at 1:00am

#858. Tequila! Women!
ID #954178 entered on March 12, 2019 at 1:03am

#857. I've Had All I Can Stands
ID #953992 entered on March 9, 2019 at 1:27am

#856. Nerd News
ID #953934 entered on March 8, 2019 at 12:39am

#855. Jersey Devils
ID #953874 entered on March 7, 2019 at 12:23am

#854. You Get A Shiver in the Dark
ID #953793 entered on March 6, 2019 at 1:00am

#853. Mere Flesh
ID #953725 entered on March 5, 2019 at 12:25am

#852. Making Money
ID #953670 entered on March 4, 2019 at 12:29am

#851. Conspiracy
ID #953597 entered on March 3, 2019 at 12:16am

#850. I Know
ID #953528 entered on March 2, 2019 at 12:22am

#849. New Quarker
ID #953454 entered on March 1, 2019 at 12:06am

#848. Journeys
ID #953345 entered on February 28, 2019 at 12:43am

#847. Life
ID #953251 entered on February 27, 2019 at 1:10am

#846. Occam's Drake
ID #953193 entered on February 26, 2019 at 1:27am

#845. Wuv. Twue Wuv.
ID #953132 entered on February 25, 2019 at 12:31am

#844. Can You Dig It
ID #953061 entered on February 24, 2019 at 12:21am

#843. Insert Cat Pun Here
ID #952872 entered on February 23, 2019 at 12:30am

#842. Loaded For Bear
ID #952718 entered on February 22, 2019 at 12:26am

#841. Emotion
ID #952598 entered on February 21, 2019 at 12:45am

#840. Germs! Germs! GERRRRRRRMS!
ID #952466 entered on February 20, 2019 at 1:42am

#839. Okay, I'm Drunk.
ID #952389 entered on February 19, 2019 at 12:10am

#838. Welp... We're Boned
ID #952326 entered on February 18, 2019 at 12:11am

#837. Lone Asshole Theory
ID #952190 entered on February 17, 2019 at 12:28am

#836. The Candy of the Meat World
ID #952094 entered on February 16, 2019 at 12:41am

#835. Purr Imagination
ID #952029 entered on February 15, 2019 at 12:30am

#834. Dunning-Krugerrands
ID #951954 entered on February 14, 2019 at 12:35am

#833. Resurrection
ID #951885 entered on February 13, 2019 at 12:38am

#832. Conversational
ID #951794 entered on February 12, 2019 at 12:35am

#831. Rules for Writing
ID #951705 entered on February 11, 2019 at 12:35am

#830. Bare Bones
ID #951630 entered on February 10, 2019 at 12:10am

#829. Philosophy
ID #951541 entered on February 9, 2019 at 1:08am

#828. Anonymous
ID #951470 entered on February 8, 2019 at 1:47am

#827. Mindless
ID #951375 entered on February 7, 2019 at 1:14am

#826. New York State of Mind
ID #951279 entered on February 6, 2019 at 12:08am

#825. A Big Apple a Day
ID #951214 entered on February 5, 2019 at 1:07am

#824. Streets of Philadelphia
ID #951130 entered on February 4, 2019 at 12:30am

#823. Georgia Not On My Mind
ID #951042 entered on February 3, 2019 at 1:35am

#822. Hav-a-Tampa
ID #950956 entered on February 2, 2019 at 12:31am

#821. The Quebec Carnival of NOPE
ID #950876 entered on February 1, 2019 at 12:32am

#820. Time to Panic
ID #950805 entered on January 31, 2019 at 12:42am

#819. Challenge Complete
ID #950746 entered on January 30, 2019 at 1:59am

#818. Cold Hands, Cold Heart
ID #950674 entered on January 29, 2019 at 12:32am

#817. Schadenfreude
ID #950612 entered on January 28, 2019 at 12:54am

#816. January So Far
ID #950542 entered on January 27, 2019 at 1:01am

#815. The Final Countdown
ID #950466 entered on January 26, 2019 at 12:58am

#814. Just the Facts
ID #950403 entered on January 25, 2019 at 12:41am

#813. On Writing
ID #950325 entered on January 24, 2019 at 12:56am

#812. One Year
ID #950256 entered on January 23, 2019 at 12:02am

#811. Next of Kindle
ID #950183 entered on January 22, 2019 at 12:11am

#810. We Need Space
ID #950101 entered on January 21, 2019 at 12:31am

#809. Historical Witness
ID #950038 entered on January 20, 2019 at 12:46am

#808. Unnatural
ID #949965 entered on January 19, 2019 at 12:48am

#807. Food for Thought
ID #949906 entered on January 18, 2019 at 12:31am

#806. Rage of Aquarius
ID #949810 entered on January 17, 2019 at 12:21am

#805. Can't Stress Enough
ID #949749 entered on January 16, 2019 at 12:29am

#804. It's a Trappist!
ID #949681 entered on January 15, 2019 at 1:00am

#803. The Apprentice
ID #949599 entered on January 14, 2019 at 12:38am

#802. Rule Britannia
ID #949536 entered on January 13, 2019 at 12:14am

#801. Talent
ID #949466 entered on January 12, 2019 at 12:46am

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