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Tuesday, Jul. 2, 2024

12:13pm 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

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#2143. It Was Aliens
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#2142. Revisited: "Good and Gooder"
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#2141. Listen to the Music
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#2140. Monkey!
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#2139. Ubeer
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#2138. Wine Ding Road
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#2137. Snip
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#2136. Eh? Okay.
ID #1040005 entered on October 31, 2022 at 12:01am

#2135. Uncertainty Principle
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#2134. A Positive Thing
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#2133. Simulation Stimulation
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#2132. Battle of the Budget
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#2131. Quantum Horseshit
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#2130. We Named the Dog "Indy"
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#2128. No Geese Involved
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#2127. Smackdowns
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#2126. It's not in Seine
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#2125. Against the Grain
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#2119. Tasting Red
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#2115. S'more and more
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#2114. Smells Like New Jersey
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#2112. Daube Glacé
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#2102. Alpha and Omega
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#2096. Another Avocado Article
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#2094. Putting the Auto in Automobile
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#2092. On Time
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#2091. Dream Weavers
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#2090. I Wood Knot
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#2089. Gut Wrenching
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#2088. Math is Easy
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#2085. More Time
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#2084. Houses of the Holy
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#2083. The Devil's Avocat
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#2082. Going Out
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#2081. The Heat is On
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#2080. Out Of Time
ID #1037330 entered on September 5, 2022 at 12:01am

#2079. Cut Me Some Slack
ID #1037286 entered on September 4, 2022 at 12:15am

#2078. Philling the Whole
ID #1037249 entered on September 3, 2022 at 12:18am

#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
ID #1037049 entered on August 29, 2022 at 12:01am

#2072. Past Tense
ID #1037010 entered on August 28, 2022 at 12:03am

#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
ID #1036196 entered on August 7, 2022 at 12:01am

#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
ID #1036041 entered on August 3, 2022 at 12:01am

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