Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ October ► 2022
S	M	T	W	T	F	S
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30	31
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Tuesday, May. 7, 2024

9:08pm EDT

Members: 950

Guests: 807

Total Online: 1,757

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:

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
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

May 3, 2024 at 11:58am
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

October 1, 2022 at 12:02am

#1038403

Muddy Talks

I'm participating in "Journalistic Intentions"

[18+] again this month, so some of my entries will be prompts from that activity.

This is one of them—as usual, selected at random.

Locks, dams, and the future of the Mississippi

When I was in Minneapolis in the summer of 2021, I got to see some of these locks and dams up close. I wrote, briefly, about it at the time: "Dam It"

So apparently, based on the link above, there's talk about removing some of them. Not the ones I toured, but downstream from there.

You might think that, being a civil engineer whose whole thing was hydrology, I'd have an opinion on it. After all, I have opinions on plenty of things that I know far less about. But you'd be wrong. Well... I do actually have an opinion, which is "they should do what's expected to have the best overall outcome." Which is why we have people do studies for this sort of thing.

If I thought about it long enough, I'd probably come to the conclusion that this should probably be my opinion on everything else, too. But no, then life would be no fun, and worse, I'd have nothing to blog about.

Besides, rivers are complicated. They build dams for reasons: flood control, erosion prevention, power, recreational purposes; usually some combination of these things. There's always a trade-off too, like when the dam blocks fish spawning or whatever, or the resulting lake drowns a community.

Left to its own devices, a river will shift over time. Not just geological time, but often in one human lifetime. You can see the effects if you look closely at a map of the rest of the Mississippi: horseshoe bends where the river once flowed, and down the center of which a state line was surveyed, have gotten cut off, leaving, for example, a bit of Tennessee on the Arkansas side of where the river is now. Several bits, actually. Some of that might have been due to Army Corps projects, but probably there was also some non-human-caused shifting over the years. If you wanna see, look up Memphis on Google Maps and then scroll north.

And I'm not saying this is bad, or good; it just is. We modify rivers for our own purposes, and for a long time we didn't think much about the consequences. Now that they're modified, though, there are consequences to unmodifying them, as well.

Even further downstream, in Louisiana, the primary Mississippi discharge has been trying to shift over to the Atchafalaya river (no, I can't pronounce it, either). If it weren't for levees and locks and whatnot—engineering projects—it probably would have switched channels by now. From what I understand, it used to switch back and forth every thousand or two years. As one channel silts up, water flows to the other, and vice-versa.

This, of course, would leave New Orleans dry (if not high), so there are economic reasons not to allow it. But there are probably good solid ecological reasons to do so. But we're a part of the ecology, too, part of nature, and we have to make decisions based on incomplete information.

I'm just glad it's not my job.

1 Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted Writing.Com, its affiliates and its syndicates non-exclusive rights to display this work.

Printed from https://www.writing.com/main/profile/blog/cathartes02/day/10-1-2022