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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 1, 2019 at 12:23am

#957959

Mayday

Hooray, hooray, the first of May!
Outdoor fucking begins today!

It's a new month, so it's a good time for me to get back to daily blogging. Maybe. (Pun intended, as always.) I'm participating once again in "30-Day Blogging Challenge ON HIATUS"

[13+]

Crazy as it may sound, we are now officially 1/3 of the way through 2019. Write about some of your goals and plans for the remainder of the year. What are you looking forward to?

I'm wary of making goals. Or plans. When I inevitably don't fulfill them, I get even more wary next time.

I'll tell you what I'm looking forward to, though: warm weather. I'm pretty sure we'll get some of that. While my area was spared the recent unpleasantness that happened in some of the middle states, I got tired of the cold weather damn quickly.

In previous entries, I've outlined my dislike of the cold. "So, Waltz, why not just move?" Well, true, I could, but apart from a few months out of the year, I rather like it here in Virginia. I've been all over the country (except for Nebraska, Alaska and Michigan, none of which are in the top 40 candidates for states to move to anyway), and while I enjoy certain places, I'm happy to merely visit. Too much traffic most places, except for where there's nothing around, in which case there's nothing around. Here, there are nearby purveyors of fine alcoholic beverages, and I don't have to sit in traffic (or, more precisely, sit in a rideshare vehicle which is sitting in traffic) to get to them.

But that's not the question, is it? To misquote an entirely too popular catchphrase, summer is coming. And, for the most part, I intend to sit here on my deck and enjoy the utter lack of snow. Assuming, of course, we don't get a volcano, nuclear war, or meteor strike that blots out the sun.

Patient and sharp readers will have noticed an inconsistency here. I rant about cold weather, and then I rant about the accursed daystar. Well, I'm not required to be consistent. Self-contradiction only makes me more interesting, right? "I am large; I contain multitudes."

This is easily resolved, though: I only go outside to sit on the deck, which has a patio umbrella. I am within two feet of the door to my house at all times, and if the blasted fusion sphere starts to annoy me, I can go inside where it's properly air-conditioned.

Still, getting back to plans, I'm hoping to do a bit more traveling this year. Maybe go to Vegas in August or September. Almost certainly visit California in December, if it's still there. Apart from that? Stay warm for as long as I can, until the cycle turns again.

And write. Against all odds and expectations, I've been steadily participating in "I Write in 2019"

[E]. Just 8 more months of that to go...

8 Like • Comment • View 7 comments

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