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Thursday, May. 9, 2024

12:06pm EDT

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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:

Elisa the Bunny Stik

about 2 hours ago
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

about 21 hours ago
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

a day ago
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

🌕 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

February 1, 2024 at 11:19am

#1063273

And It Was All Yellow

Well, here we are: the worst month of the year. At least it's shorter than other months. Wait, this is a leap year? Rats.

No sense dwelling on it. I'll just pick another site from my queue to blog about, and move on.

One perfectly legitimate reason to avoid having kids, besides the obvious ones, is that, at some stages, they ask awkward questions that may be hard to answer in an age-appropriate manner.

Like this one.

Why is Gold yellow? Spoiler alert: Einstein again
It turns out you don't have to look further than gold jewelry to experience Einstein's relativity.

I don't think I ever asked my dad that particular question, but I did ask the classic "why is the sky blue" one, and his lengthy scientific explanation went right over Kid Me's little head. I think I might even have fallen asleep.

Eventually, I understood the reason for the effect, at least to some degree. And I've often wondered why gold appears, well, gold-colored, when most other metals (with some obvious exceptions, like copper) are various shades of gray. Just haven't wondered enough to be arsed to look it up. Then this article somehow got my attention.

You’ve probably not given it much thought, but the reason why gold is yellow (or rather, golden) is deeply ingrained in its atomic structure — and it’s because of something called relativistic quantum chemistry.

Now, here's the thing: Generally (pun intended), relativity deals with large-scale things, while quantum mechanics deals mostly with the smallest. I'm told the two theories are both well-supported; that is, predictions they make turn out to match observed evidence. And yet, they're incompatible with each other (again, just going by what I've heard, here). So for me, the phrase "relativistic quantum chemistry" is itself a shiny gold thing that I just have to pick up.

Simply put, because it’s a very large atom, gold’s electrons move so fast that they exhibit relativistic contraction, shifting the wavelength of light absorbed to blue and reflecting the opposite color: golden yellow.

And there you have it: the answer. Refreshing to see that at the beginning of an article. Of course, it goes on to explain that shit further, which is also good.

Incidentally, this is an entirely different phenomenon from why the sky is blue, but I can't help but notice the parallels: blue light from the sun gets preferentially scattered by air molecules, turning the sky blue and making the sun appear yellower.

Read on for a more in-depth look into the fascinating chemistry that gives this symbol of wealth and luxury its prized color.

At this point, it's less a symbol of wealth and luxury than one of overindulgence and greed. Still pretty, but come the apocalypse, all that gold you've been hoarding will be mostly useless. It's not like any survivors will need it for its amazing electrical conductivity.

Anyway. I won't bore you with too much from the rest of the article. I do think it's very accessible—probably too much for a toddler, but not for a teen or a grown-ass adult—so give it a look if, like me, you want to finally get that stubborn curiosity looked at.

5 Like • Comment • View 4 comments

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