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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:

Kåre เลียม Enga

a day ago
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

a day ago
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
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

Nov 5, 2024 at 2:55pm
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

Nov 5, 2024 at 1:16pm
In response to "Anomalies"

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

2 Like

May 4, 2019 at 12:18am

#958202

Exploring the Unknown

Stand outside for two minutes. Make a list of ten things you can smell, ten things you can hear, and ten things you can feel.

Out... outside? You mean, like... not inside? You want me to go what now?

Fortunately, it is midnight; the accursed daystar is on the other side of the planet.

So, fine, I'll do the exercise.

Ten things I can smell
1. Tobacco smoke. I figure if I'm going to venture into the Great Unknown, I might as well light up a cigar while I'm out here.
2. The remains of the "present" one of my cats left me.
3. Pollen. It's a good thing I'm not allergic, or all 10 of the items on this list would be "nothing."
4. ...Let's just say it's been a few hours since I've showered, and leave it at that.
5. Stinkbugs. To be fair, I smell them in the house, too.
6. Hm, I think one of my propane tanks is leaking. *looks at burning cigar* *shrugs*
7. Damp wood. It just freaking rained. Luckily, it is no longer raining, or I'd be skipping this exercise.
8. I could be imagining it, but I think there's a faint odor of shit, like there always is in the outdoors.
9. Oh, there it is. Some sort of flowery whiff. It is May, after all.
10. Petrichor. This is one of my favorite words, and it's all thanks to Doctor Who.

Ten things I can hear
1. My cat scratching at the door. I'm outside, so she needs to be, too. She doesn't realize it's wet.
2. Cars. Generally, in every direction, but mostly from the interstate about a mile south of here.
3. Moths trying to commit suicide on my deck light.
4. Meow. Cat's getting insistent; I think I'll go let her out.
5. Creak. Clearly, I need to oil some hinges one of these days. I've been saying that for 23 years, now.
6. The backyard neighbor's stupid fucking dog is howling again.
7. Okay, something just crashed through the underbrush in the backyard. Maybe it's a bear. Or a mountain lion. It's not a skunk; see above.
8. Next-door neighbor's heat pump just kicked in.
9. Loose water is dripping off the leaves and splattering.
10. I have no idea what that squealing noise was, but I'm pretty sure something just died.

Ten things I can feel
1. Trepidation.
2. Wet.
3. Cold.
4. A creepy, crawly sensation down my back. Oh, yeah... spider.
5. Lost, because I'm not indoors.
6. Moths crashing into me when they get bored with the light.
7. Some unidentified bug on my ankle. This is why I hate the outdoors.
8. A scraping sensation where I swatted said bug off of my ankle with my left shoe.
9. The overwhelming desire to go back inside.
10. The bottom of my laptop as I carry it back in.

2 Like • Comment • View 6 comments

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