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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 13 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 17 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.

February 7, 2019 at 1:14am

#951375

Mindless

Gotta take a break from the blog challenge. It's a great activity, but I have a backlog of blog fodder to share.

For instance:

https://www.marketwatch.com/story/avoid-these-3-traps-when-talking-to-someone-wi...

Avoid these 3 traps when talking to someone with dementia

I've noted this before, but for any newcomers, I lost both of my parents to long bouts of dementia. All told, I spent 20 years of my life dealing with one or the other. There are few things that frighten me more than the prospect of losing my mind (though I'm sure some would say that's already happened). Compared to that, death seems easy.

Everyone dies. What's hard is that some people die while their bodies live on.

Before you ask, no, I'm not all that concerned about genetic predisposition. I have no idea what my genetics are, and I prefer to keep it that way.

Anyway, I wish I'd seen something like this article before my parents started slipping away.

You’ve got great social skills. You speak clearly and listen well. Everyone loves your engaging personality.

Obviously, it wasn't aimed at me, anyway.

Prepare to encounter speakers who repeat themselves (asking the same question every few minutes) and make illogical statements or faulty observations. Their emotions can swing wildly from moment to moment, leaving you wondering what could’ve triggered an angry outburst or crying spell.

This is true.

Say the individual ponders the whereabouts of their spouse. If you point out that their spouse has died, that may be true but unhelpful.

That seems obvious, but I can be oblivious. Now, I may have spent my life in the Regretium mines of Regretistan, but the one regret that stands out to me above all others is the time when my father did exactly that. And I answered without thinking. Or feeling.

My parents had been together for nearly 60 years when my mom died. They weren't in what I'd now call a functional relationship, and yeah, I'm dealing with the psychological repercussions of that (just like everyone else is), but they stuck together anyway. When my dad had no choice but to seek a suitable care facility for her, he went to visit her every goddamn day.

I can only hope that he quickly forgot the incident, along with my name (which is something that he was always kind of fuzzy on anyway) and, later, everything else. But I never did.

Yeah, I'm putting this out here in hopes that I can move on. Still, I could have been better. It wasn't out of anger or frustration, or anything like that - at least I don't think it was - but rather just thoughtlessness on my part. I wrote here some time ago that I feel I should work on being more compassionate; this is why.

I'll say this, though. Some people think that Alzheimer's and similar conditions strips a person to their bare essence. I've seen a lot of people with dementia getting angry, lashing out, becoming violent and hateful, like their public face is but a thin veneer hiding some horrid monster. Honestly, I don't know - I think we're all part caring and good, and part spiteful and angry, all at the same time. We are large; we contain multitudes. But in all the times I visited my father in his final years - which, admittedly, weren't as many as I should have - I never saw his dark side (and when he was in his prime, he definitely had a dark side). I'd sit down while they were eating, and he'd offer me some of his meager food. One time he saw I wasn't wearing a coat and insisted I take his. This was true even when he didn't know who I was.

Why am I terrified of dementia? Well, partly because when I'm weighed in the same balance, I'll be found sorely wanting.

4 Like • Comment • View 4 comments

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