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 4, 2024 at 10:31am

#1074760

Revisited: "NaNomaterials"

Today's peek into the past takes us back to September of 2018, and discusses a certain novel-writing month: "NaNomaterials"

Ever since I first heard of NaNoWriMo, I've been conflicted.

I'm not really conflicted anymore; I just don't care enough to put in the necessary work.

I don't generally jump on bandwagons. If something becomes popular, I view it with a certain amount of distrust.

What's worse is that there are things I like that are popular. And I absolutely hate it when people assume that I like it because it's popular.

Yeah, I joined Facebook pretty early on, but I'm not active there anymore.

I can't even get into my account long enough to close it.

And the first time I heard about Twitter, someone told me that some guy had rigged his office chair to tweet every time he farted. I swore then I would never be a Twat (or whatever they call people who go to Twitter), and nothing I've heard about Twitter since then has convinced me it's gotten any classier.

Clearly, it's only gotten worse since that entry. It's not Twitter anymore, for starters, but X. Or, as I call it, Xitter (where the X is pronounced like sh). A post on the site is called a Xit (also sh).

And no, this isn't some hipster thing for me. I won't join that group, either.

I was hipster before it was cool. Then I stopped.

There follows a promotion for "October Novel Prep Challenge"

[13+], which I still recommend to anyone planning to do NaNo (or just want some help and motivation in getting a story together).

Anyway, I'm trying to decide whether to attempt it this year. Of the three I've completed, two of them are crying out for sequels (or, really, continuations to make them 100,000 word novels), and I've got a couple of ideas for new ones, though none are very compelling to me.

Here it is six years later, and none of them have been edited yet.

Of the three I've done, one's straight science fiction; one's contemporary fantasy; and the latest is, well, not a serious attempt at getting anything publishable done - it's science fiction erotica. Naturally, that's the one I most want to continue with, and it's the one least likely to get read.

I spent so much effort world-building that last one that I've considered setting more serious fiction in that universe. "Considered" being the key word. The title of the entry was meant to be a pun on a science fiction trope, one which, like much SF, is entering consensus reality.

So why start something new when I can't finish what I've already got going?

On the other hand, if I can't finish what I've already got going, why not start something new?

Not this year, though. I expect to be traveling during October, and recovering during November.

5 Like • 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.