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Wednesday, Nov. 6, 2024

6:52pm 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

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

Show Recent Comments

10 Most Recent Blog Comments:

Turkey DrumStik

about 9 hours ago
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

a day ago
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

a day ago
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

JayNaNoOhNo

a day ago
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

tj-turkey-jobble-jobble-hard-J

Nov 4, 2024 at 6:33pm
In response to "It's Hard Not To Scare"

Smarter mice? Just what we need!

1 Like

Wordsmitty ✍️

Nov 4, 2024 at 12:22pm
In response to "It's Hard Not To Scare"

"Friendly neighborhood spider-goat." Isn't Marvel working on that for release in '26. - "Yes, it's cute, MJ, but you shouldn't ..."

2 Like

tj-turkey-jobble-jobble-hard-J

Nov 3, 2024 at 3:52pm
In response to "Revisied: "Inevitable""

I can think of far more absurd ways to die, but most of them involve alcohol and maybe prostitutes... This statement reminded me of the passing of a friends grandfather; he died of a heart attack while intoxicated and with a prostitute, Viagra also aided in his heart failure.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:46am
In response to "She Said Spatchcock"

You can spatchcock, or butterfly, any bird.

That bit might only be funny if you're familiar with British slang.

It's really a pity that the British national team's mascot is a lion and not a rooster. Ironically, that's the French national team's mascot, which did make for a pretty good joke during the Olympics.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:31am
In response to "Cave In"

tj-turkey-jobble-jobble-hard-J

-Yeah, those instigators from Illinois and Texas would really degrade the standards of Hell.

2 Like

Turkey DrumStik

Nov 3, 2024 at 9:30am
In response to "Revisied: "Inevitable""

Though I clicked on it to check, I no longer follow that site and want nothing to do with them, which is why we haven't had any LitHub links in over a year.

Well, now my curiosity is piqued. What happened on this front?

2 Like

March 16, 2022 at 12:23am

#1029004

It Was a Dark and Stormy Day

Yes, I'm running a little late today. Yesterday, because of *gestures vaguely at everything* I mixed spiced dark rum and ginger beer in copious quantities and drank it.

It was a Dark and Stormy day.

Consequently, I passed out completely, for several hours. I don't have a link, or a prompt. I suppose I could just wait until later, but where's the fun in that? I'm not sure if I'm hung over or still drunk. I do know that, thanks to the ginger beer I suppose, I'm feeling pretty good, all things considered.

Now, a proper Dark and Stormy also includes lime. But I didn't think ahead like that. Sometimes I'll buy limes, then not use them, and find them later, hard and shrunken, tucked way back in the fridge. Most of the time, though, I'll get it in my head to drink something that requires lime, such as a gin and tonic, and naturally, those times, there are no limes in the house.

I wish someone would invent stasis fields so that limes can keep fresh indefinitely. Forget warp drive, communicators, transporters, replicators, and world peace; the most important invention from Star Trek would be the stasis field.

Okay, it's actually from Niven, or possibly some SF writer before him, but my point remains.

Anyway, where was I? Oh, yeah, Dark and Stormy.

Technically, only Gosling's Black Seal rum can be used in a Dark 'n Stormy. Fortunately, I wasn't making a Dark 'n Stormy; I was making a Dark and Stormy. The rum I used was Kraken, which helpfully has a drawing of a multi-tentacled sea monster on the label, and is apparently made in Indiana; the ginger beer was from Stolichnaya, which, no, is not Russian; it's Polish, so don't give me shit about virtue signaling.

So even those ingredients were nonstandard; a proper Dark and Stormy should be made with Caribbean rum and Caribbean ginger beer.

At this moment in history, though, I don't give a shit.

Even in the depths of a binge, though, I'm still doing science: what, I wondered, is the best ratio of rum to ginger beer? I think most recipes give a proportion of 1:3 or 2:5. I tried 1:2, 1:3, and 1:1, among other mathematically in-between attempts. Admittedly, by the time I was done, I was finding it hard to do proportions. In the end, I suppose it's a matter of taste: do you want more spiced rum, or do you want more of the spicy, tingly taste of ginger beer?

1:3 seemed to do it for me, but like I said, I was lacking the cooling, tart effects of lime in the drink.

So that was my day. Very productive. How was yours?

4 Like • Comment • View 9 comments

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