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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 Enga in Montana

about 11 hours ago
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

about 16 hours ago
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

a day ago
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

July 7, 2020 at 12:12am

#987434

You're My Inspiration

Hey, it's this "inspiration" thing again.

Also, yesterday's Mini-Contest winner announced below.

PROMPT July 7th

What do you do when you are out of inspiration or ideas?

I look at prompts, of course.

Well, that's for blog entries and most of my fiction and poems. When I'm not in a blog challenge month, I have web links I can post here and comment on. Keeps me busy.

I have written a few stories and poems that weren't prompted, but the bulk of my work comes from "The Writer's Cramp - Poetry Week"

[13+] or other contests with their prompts.

Occasionally, very rarely, someone else will write something that makes me want to create a thing. I mention this because it just happened recently: "Procrastination"

[E]

That particular one was ironic because I jumped right into writing it, instead of my usual thing which is to wait until later, after which I forget about it. In other words, I didn't procrastinate writing a limerick titled "Procrastination."

You know what the toughest thing for me is? Newsletter editorials. There are no prompts, only the topic of the newsletter - for me, Fantasy or Comedy. Don't get me wrong -- once I settle on a subject, the words usually flow well enough. But I've been editing both newsletters 13 times a year for about 13 years, now, and sometimes I agonize over what to write about right up until the deadline. Okay, sometimes past the deadline; see the above poem.

And yet, having done it for 13 years, I'm sure I've duplicated earlier ideas more than a few times. That's usually okay; with more experience comes different perspectives on the subject.

What's also hard for me is coming up with prompts in the first place. I mean, if it weren't, I'd write more, right? Instead, about once a week, I have to come up with something for other people to write about. Generally it's about whatever's on my mind right at the moment; the problem with that, these days, is that my mind generally cycles between "pandemic" and "beer." The former is overdone, and the latter excludes people who prefer to keep their writing below 13+. I'd rather be inclusive with the Cramp.

So yeah, inspiration comes to me rarely and fleetingly, so I try to catch it when it zips by. But, as any professional writer (e.g. Not Me) might tell you, it's not about inspiration or ideas; it's about doing the work. And that's where I fail.

Mini-Contest results!

Some great answers yesterday, where I asked for examples of when presenting both sides to a controversy can be a Bad Thing. Since I mentioned my newsletter editorials above, I had some vague memory of writing about this sort of thing in a Comedy editorial -- and behold, I managed to find it: "Both Sides"

I felt that the closest thing to what I was talking about was the comment provided by Charlie ~:

I mean, a good example of "false both-sidedness" is vaccines. We have scientific evidence that vaccines work with little to no harmful effects, especially when taking into consideration all the good they do. When you present one side as someone saying, "Vaccines are pointless! When is the last time you met someone with [insert disease that has been mostly eradicated due to vaccines]" it's like, yeah, that's the ENTIRE point of vaccines and it's proof that they work.

Those situations annoy the hell out of me because the one side isn't actually presenting anything reasonable or sensible. Their side is, "I feel like I'm special and shouldn't have to protect my children or the rest of society from illness."

Admittedly, it didn't hurt that this was one of the specific topics I had in mind when concocting my "flat-earth" hypothetical example. But as usual -- I appreciated all of the comments, and you'll all get another chance in a few days. But this week's Merit Badge goes to Charlie ~

14 Like • Comment • View 11 comments

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