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Saturday, May. 4, 2024

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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:

Kåre Enga in Montana

about 23 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

a day 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

May 2, 2024 at 11:37am
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.

December 21, 2021 at 12:02am

#1023471

Exit Night

With over 1800 entries in this blog, I'm pretty sure I've repeated a blog title before, though I haven't gone searching for duplicates, so I don't know when it might have happened.

This problem is only exacerbated on important dates, like my birthday or the winter solstice, both of which I tend to bang on about when they happen.

And today is the winter solstice, at 10:59 am in my time zone.

Hence the twisting of a Metallica lyric in my title today; I'm pretty sure I've never used that one.

It has been my personal tradition, for a while now, to stay awake between sunset and sunrise on the longest night of the year. I do this to remind myself that "even the darkest night will end, and the sun will rise."

As an aside, I can't be certain that tonight is the longest night. The information I found goes only to the minute, and the number of minutes is the same tonight and tomorrow night (though today will definitely be the shortest daylight of the year). I'm sure I'd know if they broke it down to the second. Either way, though, the difference, if there is one, is measured in seconds so it hardly matters. I'm only pointing this out because I like to get these technical matters straight.

This staying up through the longest night thing is something I try to do but don't always have the opportunity.

Sometimes, I'm traveling, and that's not conducive to staying up all night. Well, I'm not traveling this year.

I vaguely remember that one year, I had a cold, and so I didn't do it, because that would suck. One requires rest when one is ill. But I don't have so much as a sniffle right now (which is weird, because usually winter makes my sinuses act up even if I don't have a cold or you-know-what).

This year, my excuse is that I'm between eye surgeries -- as I noted, I had my left eye done on Thursday, and the right eye is scheduled to get poked at this coming Thursday. So no, I'm not going to attempt it tonight. My sleep is disrupted enough this week, as I'm pretty sure I mentioned a couple of days ago.

But I have to mark the occasion in my mind, anyway, and yesterday, I realized that I already had. The moment of sunrise on Solstice day is like a rebirth or renewal for me -- as I've said before, quoting Doctor Who, it's the moment I know that we're "halfway out of the dark." Well, I had a moment like that on Sunday, instead.

See, before I go see a movie, I sit at the theater bar and drink some beer. These past few months, I've had to take a picture of the menu on the wall and order from the image on my phone, because the writing on the wall was just too blurry for me to read -- but I could see fine up close. Being able to read beer menus on walls is an important life skill for me, and not being able to do it makes me feel like I'm too old and decrepit to be there. ("Don't they have printed menus?" "Yes, but they can't be arsed to keep them up to date.")

Well, before I went to see West Side Story, I sat down at the bar and... I could read everything on the menu. Even the small print, like ABV and prices. Though only out of my left eye.

So yeah. I'm halfway out of the dark.

6 Like • Comment • View 4 comments

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