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Friday, Apr. 19, 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

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 ✍️

a day ago
In response to "Down Under"

Water? What about where their sewage waste goes?

1 Like

Elycia Lee ☮

Apr 16, 2024 at 10:43am
In response to "What's the Difference Between a Duck?"

So happy that there is an answer to that Alice in the Wonderland riddle.

Finally. Fascinating stuff. All of them. There is something rather philosophical about comedy. You are certainly right there.

Elisa the Bunny Stik

Apr 15, 2024 at 8:35am
In response to "That's Cole"

"I don't know what the latest fad food is, but I can almost guarantee that behind the fad is someone with money trying to make more of it."

I'd say there are multiple fad foods, including goji berries. That said, cauliflower became trendy in 2018 and has maintained some level of staying power. I still see cauliflower rice as an option in many places across the US.

4 Like

Elisa the Bunny Stik

Apr 13, 2024 at 6:10am
In response to "Mawwiage..."

"Or, at the very least, it's an emotional bond more than a business arrangement."

And for a substantial subset of parents, it's neither. They either just want kids to show off like trophies or dive headfirst into various forms of abuse.

3 Like

Aennaytte: Free & Wild in GoT

Apr 12, 2024 at 12:39pm
In response to "Coincidences"

Some words even cross species.

My golden cat calls me Mom frequently.

1 Like

tj ~ endeavors to persevere!

Apr 11, 2024 at 1:58pm
In response to "A Cinderella Story"

Do you mean something like Carl having to work in the garage for his wicked step-dad while his brothers party? He was polishing an old hubcap that was magical and the next thing he meets a rich cougar at the club but has to leave by midnight when the spell wears off. As he exits he looses a boot. The cougar takes the boot with her and ends up having car problems the following day and stops at the garage where she notices Carl sweeping the floor with only one boot. She hands him the boot, it fits, and they are last seen sailing off on her yacht.

1 Like

tj ~ endeavors to persevere!

Apr 11, 2024 at 1:48pm
In response to "Things Go Better With Cahokia"

I bet they left because there wasn't anymore deer to barbecue.

2 Like

Robert Waltz

Apr 10, 2024 at 11:05am
In response to "Dark Side of the Moon"

⭐️Jellyfish⭐️

: Also known as a swag bag, but I usually prefer alliteration to rhyme (and also, since I pretend to be a writer, I like coming up with my own terms). No idea what you call them on that side of the pond. It's not technically "bling" because there wasn't any personal decoration, but it had things like certified sun-gazer glasses, a copy of their special eclipse bottle label art, a winery-logo corkscrew, and some delicious truffles (the chocolate kind, not the mushroom kind). Kind of like a Christmas stocking, but in April and for wine and astronomy nerds.

⭐️Jellyfish⭐️

Apr 10, 2024 at 8:18am
In response to "Dark Side of the Moon"

Wine, an Eclipse, and Pink Floyd Playing - Literally sounds like a Perfect Day!

And A Bling Bag! (Although not sure what this is, I am thinking a bag full of sparkly jewellery which it probably isn't)

1 Like

Kåre Enga in Udon Thani

Apr 10, 2024 at 1:34am
In response to "Dark Side of the Moon"

It's nice you took time out from you routine life and routine blogs. Mind you, routine has some appeal.

I saw the eclipse in 2017 in Montana. I'll probably not see another. Do I care? Well... if I happen to be near one... sure. I missed the lunar eclipse last year in Thailand and I wasn't happy... but I saw one in Venice (even saw Mars).

I agree that a sports venue has an ambience that one loses at an impersonal distance. I was in Allen Fieldhouse when Kansas won the national basketball championship in 2007. Not the same as being at the game, but close. 10,000 fans created some ambience. And the town afterwards? Incredible!

Video is visual/audio at best. But what is the smell, the touch of a breeze, a hot dog or the taste of wine on the lips? Also... one only sees/hears what others see/hear. I want to have my own experience.

Songkran is soon, in three days. I dread it in some ways, but it may be a break from the ennui of hot at night and worse by day.

1 Like

March 20, 2019 at 12:43am

#954627

Balance

Today is the equinox.

You might have heard stuff about the moon tonight too. "Super moon" they call it. There's some science behind this, but as always, popular descriptions of it show up highly exaggerated. Here's a link to a pretty good explanation.

https://earthsky.org/?p=301190

Just to clear some things up:

No, you can't balance an egg today and only today. That's idiotic.

You won't even notice the slightly larger moon. But that shouldn't stop you from taking a few minutes to look at it. Anything to get people looking at the sky is a good thing.

I'm not going to go into my usual rant about Blue Moons (of which there is one coming up in a couple of months). From the above article:

Last but hardly least, this March 2019 full moon gives us the first of four full moons in one season (between the March equinox and June solstice). Most of the time, a season – the time period between an equinox and a solstice, or vice versa – only harbors three full moons. But since this March full moon comes very early in the season, that allows for a fourth full moon to take place before the season’s end.

Some people call the third of four full moons in one season a Blue Moon. So our next Blue Moon (by the seasonal definition of the term) will fall on May 18, 2019.

By which they mean that correct people call this the Blue Moon. The other definition:

The next Blue Moon by the monthly definition – second of two full moons in one calendar month – will come on October 31, 2020.

...is, simply, incorrect; and that's all I'm going to say about it here. I've ranted enough about it elsewhere. Still, it's something to look forward to next year: a full moon on Halloween. No meaning to it, unless you've read a certain book by Roger Zelazny, but it's cool anyway.

Again, if it makes you go look at the Moon - fine.

Bottom line: Here in the Northern Hemisphere, soon it will be spring. Finally. Naturally, I saw a weather report for freezing temperatures here next week, so my satisfaction at this change of season is tempered by that.

On a personal note, it was on the solstice that I committed to eating less and exercising more in an effort to lose weight. All I'll say about that is that I've been successful - so far. Eventually, I will fail. And yeah, I had a couple of overindulgences over the past three months, but I've always managed to get back on track.

It won't last, but it's something of an accomplishment for me.

Edited to add:

At this moment, the link above isn't working properly. It's not my fault. But this is pretty cool too. https://apod.nasa.gov/apod/ap190320.html

5 Like • Comment • View 4 comments

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