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Wednesday, Apr. 24, 2024

9:56pm 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

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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 "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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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?

Aennaytte: Free & Wild in GoT

a day ago
In response to "Going to the Dogs"

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

#2077. Keep Wining
ID #1037199 entered on September 2, 2022 at 12:11am

#2076. Intelligence Gathering
ID #1037153 entered on September 1, 2022 at 12:34am

#2075. Vulgar Tongue
ID #1037122 entered on August 31, 2022 at 12:04am

#2074. Complexity
ID #1037088 entered on August 30, 2022 at 12:03am

#2073. Fly the Trendy Skies
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#2072. Past Tense
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#2071. Lucky Strikes
ID #1036983 entered on August 27, 2022 at 12:02am

#2070. Woolly Bully
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#2069. Sodium Cool
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#2068. Peeling Out
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#2067. Nonsense
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#2066. Weight a Minute...
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#2065. A Fine Selection of Bumfodder
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#2064. Marginal Utility
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#2063. Now Lie In It
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#2062. Orange You Special
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#2061. Business Development
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#2060. Probe
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#2059. Labor
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#2058. Punday
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#2057. Medical Leeches
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#2056. So Low
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#2055. Measure By Measure
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#2054. Loose Morels
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#2053. Camus For You
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#2052. Ah, les œufs
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#2051. Milking It
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#2050. Can't Budge It
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#2049. Logos
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#2048. Off the Edge
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#2047. Books, Some
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#2046. Hallelujah
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#2045. That's Mental
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#2044. Big Dick
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#2043. Grueling
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#2042. Mommy
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#2041. Enough
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#2040. Enablers
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#2039. A Crystal in Time
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#2038. The Disconnected You
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#2037. Home on Deranged
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#2036. No Way Home
ID #1035578 entered on July 23, 2022 at 12:01am

#2035. Heated Discussion
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#2034. Punctuated
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#2033. Brain Fart
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#2032. Smiley
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#2031. Lift Me Up
ID #1035341 entered on July 18, 2022 at 12:01am

#2030. Ennui and Off-we
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#2029. History of the Mundane
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#2028. Now You Know Better: Food Edition
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#2027. Vive La Révolution !
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#2026. Just Once
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#2025. Imagine
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#2024. Speakers for the Dead
ID #1035020 entered on July 11, 2022 at 7:06am

#2023. Dashing
ID #1034966 entered on July 10, 2022 at 12:03am

#2022. Golden Age
ID #1034910 entered on July 9, 2022 at 12:03am

#2021. Negative Is Positive
ID #1034851 entered on July 8, 2022 at 12:01am

#2020. Old Rasputin
ID #1034803 entered on July 7, 2022 at 12:02am

#2019. Propaganda: A Socially Correct Goose
ID #1034755 entered on July 6, 2022 at 12:02am

#2018. That's Hollywood
ID #1034711 entered on July 5, 2022 at 12:02am

#2017. The Fourth Is Strong In This One
ID #1034670 entered on July 4, 2022 at 12:01am

#2016. Exoplanets
ID #1034629 entered on July 3, 2022 at 12:02am

#2015. Damson In Distress
ID #1034573 entered on July 2, 2022 at 12:01am

#2014. Can't Sleep, Clown Will Eat Me
ID #1034498 entered on July 1, 2022 at 12:02am

#2013. The 80s Called
ID #1034460 entered on June 30, 2022 at 12:01am

#2012. Gut Feeling
ID #1034432 entered on June 29, 2022 at 12:03am

#2011. Not for the Faint of Art
ID #1034377 entered on June 28, 2022 at 12:01am

#2010. Jaded
ID #1034326 entered on June 27, 2022 at 12:01am

#2009. The Yeast of Us
ID #1034295 entered on June 26, 2022 at 12:01am

#2008. Food Psychology
ID #1034210 entered on June 25, 2022 at 12:02am

#2007. Everyone Calls Me Mushroom Because I'm Such A Fun Guy
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#2006. Queen of Sheba
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#2005. Brutal
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#2004. We're Doomed.
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#2003. Lousy Lurks
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#2002. Frickin Lasers
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#2001. Are You Game?
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#2000. Fuzzy Tales
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#1999. That's Reasonable
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#1998. Egg Sellent
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#1997. The First But Not the Last
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#1996. Bar Wars
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#1995. In Pursuit
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#1994. Death Do Us Part
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#1993. Drink of the Gods
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#1992. Got Me Doing It
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#1991. Not So Far Away
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#1990. Let's Freeze More Peaches
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#1989. Utopia
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#1988. Natural Philosophy
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#1987. Beer. That's Why.
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#1986. Like a Version
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#1985. Don't Do It
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#1984. Ceci n'est pas une pipe
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#1983. Misinformation
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#1982. Egg Zactly
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#1981. Food History
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#1980. Trouble
ID #1032941 entered on May 28, 2022 at 12:03am

#1979. Under the Sea
ID #1032910 entered on May 27, 2022 at 12:05am

#1978. Going Bananas
ID #1032870 entered on May 26, 2022 at 12:49am

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