Complex Numbers (Book)

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Complex Numbers

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

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Signature for those who have won a Quill Award at the 2020 Quill Awards

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10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 20 hours ago
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

a day ago
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

🌖 HuntersMoon

a day ago
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

a day ago
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

Dec 20, 2024 at 6:06pm
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

Dec 20, 2024 at 1:00pm
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

Dec 20, 2024 at 12:58pm
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

October 22, 2024 at 10:16am

#1078731

Stark and Dormy

And now, one of my rare posts about actual writing...

2024 Bulwer-Lytton Fiction Contest

It is a truth universally acknowledged that of all the bad opening lines of literature, with the possible exception of the one that begins, "It is a truth universally acknowledged," the one that begins, "It was a dark and stormy night" is the nadir of all possible opening lines. This was from Bulwer-Lytton's novel Paul Clifford, about which literally no one outside of academia knows anything apart from the opening line.

Like all truths universally acknowledged, it's not necessarily true. But it still provides the impetus for writers to try to do worse, generally to hilarious effect.

I've posted about this before, I know, but today's entry is about this year's "winners."

Now, you'll have to go to the site to see the Grand Prize Winner. Suffice it to say that I don't agree. It's bad, but not dark-and-stormy-night bad.

I'll do what that site doesn't, which is to first paste the inspiration for the contest, the actual opening line of Paul Clifford (they put it way down the page):

It was a dark and stormy night; the rain fell in torrents—except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness.

Now, some of my personal favorites:

It was a dark and stormy night, which makes perfect sense when you realize we’re on Neptune, with a mean distance from the Sun of 4.5 billion kilometers (or 30 astronomical units), and winds that howl at 100 meters per second, composed of mostly hydrogen and helium (and only trace amounts of methane), which is way better than Uranus, which stinks to high heaven.
—Jon A. Bell, Porto, Portugal

Yes, I'd probably have selected that one as the Grand Prize Loser, mostly because I'm sick and tired of seventh-planet puns, but also because of the completely unnecessary science data.

And, of course, I'm quite fond of the Vile Puns section:

"I do enjoy turning a prophet," said Torquemada, as he roasted the heretic seer on a spit.
—A. R. Templeton, Stratford, Canada

And:

"My laddies may not be the fastest sugar cane harvesters," Fergus confessed, "but they're not as slow as my lasses..."
—Mark Meiches, Dallas, TX

Just one more; like I said, the page is there to view the other stinkers at your leisure:

Ralf Smalborgson kept a small shop in Direperil, Minnesota, and his goods consisted only of medieval stringed instruments, lanyards and backstays, and some limited apothecary supplies, giving the store its uninviting signage: Lute, Rope, and Pillage.
—Ciarán McGonagle, Derry, Northern Ireland

Which reminds me of my D&D-adjacent bard, one of whose catchphrases is, "Come on, baby, fight my lyre!"

3 Like • Comment • View 2 comments

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