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Monday, Feb. 10, 2025

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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:

🌖 HuntersMoon

26 minutes ago
In response to "Paint in the Neck"

Given the current situation, maybe they'll update their logo... by changing the paint color to orange.

1 Like

tj wanderlust-words-in-motion

about 18 hours ago
In response to "Revisited: "Bloomington""

I have been to Bloomington a few times myself, the one in Minnesota, not Illinois or Indiana.

2 Like

🌖 HuntersMoon

about 23 hours ago
In response to "Revisited: "Bloomington""

You and Jim look just the same as I remember. Hmmmmmm. I was hoping my memory was fading but no.

1 Like

tj wanderlust-words-in-motion

a day ago
In response to "What's In a Name?"

It seems no matter what, someone will be offended by it. Even if no one is offended, someone will become offended that no one's offended. Maybe we should bring back All In The Family.

2 Like

🌖 HuntersMoon

a day ago
In response to "What's In a Name?"

Shhhh! Let's hope one of the Great Pumpkin's minions doesn't see this. You may get banned on the basis of... promoting transgenderism, exploiting children, or whatever the hell they come up with.

2 Like

tj wanderlust-words-in-motion

Feb 7, 2025 at 4:26pm
In response to "Roll Model"

Most commercial-grade wipe is like trying to clean one's bum with super-thin wax paper! When I see "Mega-Roll" I instantly realize it will not fit into the holder. I don't put a lot into buying butt-wipe, I stick to one product I know will fit the holder, clean the crap, and my fingers won't bust through.

1 Like

tj wanderlust-words-in-motion

Feb 6, 2025 at 3:24pm
In response to "So Much Energy"

I always thought electroweak{i/} was a bad choice of terminology. It sounds like the batteries in you flashlight are almost dead! They should have used a term like "electronuke" which sounds like some super-hero stuff. There's no need to fear, Electronuke is here!"

Also, when crossing Higg's field, beware of Higg's boson (cross between a boar and a bison) or you may get killed; unless of course, Electonuke shows up and saves your ass.

Alright, maybe I should be writing a story instead of leaving a comment...

1 Like

Graham B.

Feb 6, 2025 at 12:04pm
In response to "So Much Energy"

The only energy-carrying particle that concerns me is the Joeson, as in "I need my morning cup of Joeson to get me up." It's responsible for the strong nootropic force (for me, anyway).

3 Like

Lazy Writer est 4/24/2008

Feb 6, 2025 at 11:36am
In response to "So Much Energy"

I need to find some of that energy..because mine is worn out!

2 Like

tj wanderlust-words-in-motion

Feb 5, 2025 at 4:33pm
In response to "That Healthy Glow"

Yes, they do still make black lights, most are LED. We have one above my wife's plants, it helps them survive through the winter with our lack of sunlight. They seem to be more purple than the black lights from days gone by. Interestingly, they make our Australian Shepard glow purple (her black areas) and they make our Husky's blue eyes glow, but not the black on his fur.

1 Like

February 9, 2025 at 9:24am

#1083584

Revisited: "Bloomington"

Today's the day I usually dig into the past to unearth an old entry at random. Today, we'll take another look at a short entry I did during an ill-fated 2021 summer road trip: "Bloomington"

Anyway, I mean the one in Illinois, not the one in Indiana.

I wasn't even as clear as I could have been. The Bloomington in Indiana may be more well-known than others, but it's still probably not very famous. I almost went there for the 2024 solar eclipse, because I noticed that the path of totality passed right through the Indiana town. We ended up not far from there, though.

But, again, the entry I linked up there was about the next state over.

Hey, at least it's not Springfield. Then it could be any state. Sometimes I think it would be fun to visit every Springfield in the country...

It would be even more fun to try to find the shortest route that visits every Springfield. From what I understand, an algorithm to do something like that is a difficult computer problem.

Point is, it's extraordinarily rare that whatever they've named the place after is still there today.

Upon reflection, I shouldn't have said "extraordinarily rare." That was hyperbole at best, and misleading at worst. I do like looking into the origins of place names (as I did in that entry for Bloomington), much as I enjoy looking into etymology. But I shouldn't take wild guesses at the rarity of that sort of thing; I don't have enough data.

In any case, since it was a travel update, the entry was short and really only notable for the link that, if followed, will lead to a rare photo with me in it.

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