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Thursday, Feb. 20, 2025

3:23pm EST

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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

Show Recent Comments

10 Most Recent Blog Comments:

Adhere - Definitely Writing

about 8 hours ago
In response to "One Fine Thing"

I immediately thought of "Imfamy, imfamy, they've all got it imfamy." But then my mind does that.

1 Like

tj wanderlust-words-in-motion

about 23 hours ago
In response to "Fail to Succeed"

In one way, it's good to have people with boneheaded ideas, it provides something to blog about.

1 Like

Adhere - Definitely Writing

a day ago
In response to "Fail to Succeed"

Having drunk soda on both sides of the Atlantic, I have to say that Mountain Dew with HFCS in America tastes a lot better than the 'same' drink made with sugar here in the UK. The experience is smoother and so is the taste.

2 Like

tj wanderlust-words-in-motion

a day ago
In response to "Tater Tales"

Instant potatoes? Yes, I enjoy them, too. We also use them for thickening up soups and stews.

1 Like

Robert Waltz

Feb 17, 2025 at 11:23pm
In response to "Linguistic"

Annette

- I appreciate the recommendations, but I canceled Netflix when the choice was to put up with ads for a lower price or pay a shitload of money. If it were free with ads, I'd manage like I did in the days of broadcast TV, but I flat-out refuse to both pay money and watch commercials, which is why I never had cable TV.

The price for the ad-free experience also went up to the point where it wasn't worth it with the amount I watched.

Annette

Feb 17, 2025 at 3:40pm
In response to "Linguistic"

I refer to my three languages as three different brains. In France, I activate my French brain. Which made for some funny turns of phrase when I was speaking to my son in English with English words, but in French syntax.

Netflix has some really good multilingual TV series. I recommend

Monsieur Spade

Black Spot

Capitani

1 Like

Robert Waltz

Feb 17, 2025 at 12:00pm
In response to "Linguistic"

Kåre เลียม Enga

- yeah, I edited out the duplication, because it could be seen as a refutation of itself.

1 Like

Kåre เลียม Enga

Feb 17, 2025 at 11:32am
In response to "Linguistic"

I use translation tools all the time... and subtitles on youtube.

My French pronunciation is okay because I learned it as a child; my Spanish is okay because I practiced it. I slip into both with one key exception. French is easier when I'm depressed and Spanish can draw me out of depression.

Speaking multiple languages has also been linked to delayed onset of dementia symptoms.

Yes, I saw that you repeated that. It bears repeating.

Speaking multiple languages has also been linked to delayed onset of dementia symptoms. Or so I hope.

1 Like

Lazy Writer est 4/24/2008

Feb 16, 2025 at 3:18pm
In response to "Revisited: "Hush""

Well as someone who only hears out if one ear..I prefer to be able to hear completely any sound or noise or whatever. There are sounds you never would miss until you can't hear them anymore.

Anyway each to their own..I also prefer silence at times too.

Keep writing.

1 Like

Robert Waltz

Feb 15, 2025 at 2:57pm
In response to "Ignorance is the Opposite of Bliss"

Kåre เลียม Enga

- While competition is often touted as the driving force of progress or evolution, it's actually cooperation that's most important. Even opposing sportsball teams, while seeming to be in competition, have agreed on a set of rules, the enforcers of these rules (referees or umpires or whatever), and the penalties for breaking the rules.

The Space Race is another example. On the surface, it was a dick-measuring contest between US and USSR. Each country relied on internal cooperation, obviously, but they also cooperated with each other—if only through things like weapons treaties and promises not to go to war over it.

Competition is a factor, of course. But survival depends on cooperation.

1 Like

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