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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:

Aiva Raine

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 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

November 19, 2020 at 12:01am

#998678

Strangers in the Night

Really, isn't everyone a stranger? Philosophically speaking, I mean.

PROMPT November 19th

Share a time when an interaction with a stranger had an affect on you.

I walked into a brewpub and talked to a stranger. The stranger gave me beer and took my money. That had a wonderful effect on both of us: I got beer and she got money.

On the other extreme, one time a stranger pulled out in front of me while I was driving. My car hit his, I went to the hospital, we went to court. Those weren't great interactions, but they had an effect.

Incidentally, I wasn't seriously injured, it was entirely his fault, and I ended up with a small settlement. Car was totaled, though. Was he injured? I don't know and I don't give a shit.

In writing this, I've been trying really, really hard not to unleash my inner editor.

I have failed.

People mix up "affect" and "effect" all the time. It's something I notice when it's wrong, but I don't end up thinking less of whoever does it, not like I do with people who can't keep "its" and "it's" straight, or "there," "their," and "they're." Or how I pass judgement on people who type "loose" when they mean "lose," or "opps" when they mean "oops." Those last two are generally the same people, and I think they follow some sort of Law of Conservation of Os -- though that doesn't explain where they get the extra P from. Probably from drinking too much beer.

Anyway. As I was saying. "affect" and "effect" are often confused, because frankly they're confusing. You can affect a person, or someone can have an effect on you. Someone once said, "'affect' is a verb but 'effect' is a noun." And in those common uses, they're right... but here's the confusing part:

Affect can also be a noun. And effect can also be a verb.

Those uses are less common, it's true, but anyone following the "affect-verb, effect-noun" rule is going to be caught off guard, like when you realize just how many exceptions there are to "I before E except after C."

Example of affect as noun: "The patient's affect was consistent with schizophrenia." (yeah, this version of the word is mostly just used in psychology)

Example of effect as a verb: "With perseverance and tenacity, and a whole lot of money, we can effect change in the world."

Isn't English fun? I think it's fun. I have a great deal of affection for it, even when I'm effectively putting on an affectation of pedantry.

Speaking of "loose" and "lose," there's a similar problem there: "loose" is normally an adjective, but it can be a verb: "He loosed an arrow at the target." This is, of course, distinct from "He will lose the archery competition because he mixes up 'lose' and 'loose.'"

"Only loosers care about spelling and grammar." "You mean 'losers.'" "Your mother is a looser." "Yeah? Well, yours is looser."

And, for the record, I know these things because a series of strangers taught me English grammar and spelling when I was in school. I guess they had an effect on me.

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