Complex Numbers (Book)

Blog Calendar

◄ August ►
S	M	T	W	T	F	S
				1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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

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:

tj-Merry Mischief Maker

about 21 hours ago
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

tj-Merry Mischief Maker

a day 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🎁

Dec 23, 2024 at 12:56pm
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

Dec 23, 2024 at 10:04am
In response to "Trash Pandas"

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

4 Like

Jayngle Bells

Dec 23, 2024 at 10:03am
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:

Access Restricted

This is a private area. Access has been restricted and you may not view it under its current settings. If you feel you should have access, please contact the area's owner and request access.

Note: To contact a member via email, click the small envelope icon to the right of their handle. You must be logged into your account to send an email.

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

August 27, 2024 at 11:01am

#1075789

They Invented It; We Perfected It

In a twist of cosmic coincidence, today's article is also from Cracked and is also about opposites.

5 Words That Mean the Exact Opposite If You Go to England
Jack Reacher makes no sense, and to understand why, you need to understand British English

Clearly meant for an American audience. If a British rag had written this article, it would have been "5 Words Yanks Get Backwards."

England is a strange land, where they speak a language known as English. You might have trouble understanding what anyone there is saying.

Strewth.

For example, you might hear someone described as “mean,” and you think that refers to how they say cruel things. You later realize it really refers to how they’re stingy with money.

In fairness, those traits often go hand in hand.

5. Tabling an Issue

In America, when someone says, “Let’s table that discussion,” they mean, “Let’s stop talking about that for now.”

Except these days, you'd say "let's put a pin in that and circle back later."

In Britain, when someone wants to table something, it instead means they want to discuss it right now.

And this nicely illustrates the hazards of verbing nouns. "Take it off the table" or "put it on the table" would be close equivalents, and less ambiguous.

4. Public School

If you went to public school in the U.S., that means you went for free, in a school set up by your local government.

Generally badly.

In England, however, the term “public schools” refers to the most elite schools in the country, places like Eton and Harrow... They’re run by private institutions and charge fees.

I've known about this difference for a while, and I gotta say, in this case, I'm going to side with the US.

But it's not like either side of the pond is going to change its usage soon, so it's just important to know there's a difference. The way I remember it is that a pub, originally public house, is also privately owned.

3. The Doughnut Effect

One of the few delicacies that doesn't have a different name in the two Englishes. We say cookie; they say biscuit. They say donut too; they just don't use the lazy spelling.

However, this item isn't about delicious treats, but about how cities grow rings around them... differently in each country. Oh, just read it..

2. Luck Out

If you luck out, that means you stumbled into some good luck.

That is, obviously, the US version. As one should expect by now, the UK version is the precise opposite.

Though the character Reacher is American, the author Lee Child is British. It appears here that the author is using “luck out” in the exact opposite way from how Americans do.

I'm mostly just including this because the subhead up there called out Jack Reacher.

And this is not an invitation to discuss the literary merits, or lack thereof, of the Reacher books. Which I've never read, but I've enjoyed the Amazon adaptation so far.

1. A Moot Point

When I was a kid, I read books in both American and British English, which is why I'm largely bilingual now. But I gotta admit, this one confused me for the longest time.

If a British person says a point is moot, they mean it’s up for debate, while when an American says it, they mean it’s closed for debate.

The article actually goes into some of the semantic reasons for that, which is one reason I read Cracked.

This one's similarity to the "table" one is, however, too obvious not to comment on. But the article did that for me, too.

4 Like • Comment • View 1 comment

© Copyright 2024 Waltz Invictus (UN: cathartes02 at Writing.Com). All rights reserved.
Waltz Invictus has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.