Complex Numbers (Book)

Blog Calendar

◄ October ►
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 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🎁

about 24 hours 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:

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

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 13, 2024 at 10:31am

#1078214

Revisited: "I Wood Knot"

We're only going back two years in today's trip to the past, to a brief entry that linked an Atlas Obscura article: "I Wood Knot"

Short one today, to balance out yesterday's.

Yeah, I looked, and indeed, I'd written an entire encyclopedia entry the day before.

Quote from the article: In the Cathédrale de Saint-Pierre in Geneva, Switzerland, a high-backed wooden chair sits in a place of honor. It’s roped off so that nobody can sit in the seat, where the French preacher John Calvin sat more than 500 years ago.

I've looked more into Calvin since then, and there's almost nothing about his philosophy or theology that sits right with me. (Pun intended. Chair? Sits right? Yeah, baby, I'm BACK.)

Me: At least they're not claiming it's made of wood from the True Cross.

At least one of the innumerable churches, cathedrals, basilicae, shrines, whatever that I saw in Europe claimed to have such a splinter.

Article: From the pulpit at St. Pierre Cathedral, he preached about the importance of religious scriptures and the concept of predestination, which held that certain people were set on a path for salvation from the very beginning of their lives.

Regardless of my rejection of the theology, there's no denying that he was a major influential figure. Perhaps he was predestined to be so.

Article: The chair of Calvin is a plain-looking wooden chair with a trapezoidal base and narrow backrest.

Appropriate that it's not all gilded and ornate. Credit to him for not being too hypocritical.

Me: I just wanna know one thing:

Did it have room for Hobbes, too?

I have no doubt whatsoever that John Calvin would disapprove of that bit of levity. Any worldview that doesn't put a sense of humor high on the list of important traits is not one I can ever accept.

2 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.