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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:

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

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

December 5, 2019 at 12:03am

#970979

Observability Bias

Today's link comes to us from the UK, so be prepared for British spelling. In contrast to yesterday, it's a short one and probably more relevant to our daily lives.

https://www.theguardian.com/lifeandstyle/2017/oct/27/lonely-short-of-friends-loo...

Lonely? Short of friends? Try looking at it differently

You never see your friends at home alone in their pyjamas, eating pickled onion Monster Munch...

Okay, so I was prepared for "pyjamas," but what in the culinary hell is "pickled onion Monster Munch?" Jeez, England...

Psychologists are regularly berated for spending their workdays reaching blindingly obvious conclusions about the world... At first glance, it’s tempting to respond that way to a new study from the University of British Columbia, explaining why people tend to assume that their friends have more friends, and lead less solitary lives, than they do. Can you guess? That’s right: because every single time we see our friends, they’re socialising.

That's like every time my friends see me, I'm drinking, so they probably assume I'm an alcoholic. But I rarely drink when there aren't other people around. Don't get me wrong; I'm not averse to drinking alone - it's just that alcohol helps me socialize, but what it does not help me do is play video games, read, or follow TV shows. Perhaps if I actually wrote more, I'd drink more.

You’re never there when [your friends] wake in the dark at 3am, wondering where their lives are headed.

I'm not immune to existential crises, but this never happens to me. Is it common? Maybe it doesn't happen to me because I like to stay up until at least 3 am. Okay, that's a technicality. But in general, the only times I wake up when I ought to be sleeping are a) a cat has knocked something off of something else or b) I just had a nightmare, in which case I think, "Gah, another nightmare. Oh well. Just a dream" and go back to sleep.

So, yes, the fact that we only ever experience loneliness when it’s happening to us is blindingly obvious, I suppose. But blindingly obvious in an almost literal sense: it’s so self-evident, we barely ever see it.

I'm pretty solitary by nature, so I'm rarely lonely. I'm not even sure that I've ever experienced it in the way that others do, kind of like I'm never sure if my "yellow" is your "yellow." I like people, in general; I just can only deal with so much socializing before I have to retreat.

Anyway, so add "observability bias" to those things we have to watch out for.

Speaking of which, I'm about to travel again, so posts aren't guaranteed for the next week or so. I'm sure you'll all find a way to cope.

1 Like • Comment • View 1 comment

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