Complex Numbers (Book)

Blog Calendar

◄ April ►
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
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 7 hours ago
In response to "Sensational"

They say carrots can improve your eye sight, but it's been proven that drinking alcoholic beverages can make you see double.

After stating this, I find myself wondering why hasn't anyone tried fermenting and distilling carrots and marketing it as a vision tonic?

2 Like

🌖 HuntersMoon

about 12 hours ago
In response to "Sensational"

OK, look around you and observe (where possible) the reality of the newly revealed "facts." It's pretty clear that "Smartphones make you a hell of a lot of folks stupid."

2 Like

Elisa: Snowman Stik

about 14 hours ago
In response to "Sensational"

Thank you for reminding me to check on Retraction Watch.

https://retractionwatch.com/

3 Like

tj-Merry Mischief Maker

a day ago
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

a day ago
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

🌖 HuntersMoon

a day ago
In response to "Gray Matters"

I've always believed "better gray than gone away..."

2 Like

tj-Merry Mischief Maker

Dec 25, 2024 at 3:02pm
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

Dec 24, 2024 at 5:16pm
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

Dec 23, 2024 at 4:55pm
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

April 15, 2024 at 8:25am

#1068809

That's Cole

Not to brag, but I've known this for a long time. Still, there's always new stuff to learn. This is a fairly old article from Vox:

Kale, Brussels sprouts, cauliflower, and cabbage are all varieties of a single magical plant species

And collard greens. Also kohlrabi, but every time I mention kohlrabi people be like wut?

In some circles, kale has become really, really popular.

Too popular. I think people may have finally calmed down on it a bit since this article came out in 2015. 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.

Once a little-known speciality crop, its meteoric rise is now the subject of national news segments. Some experts are predicting that kale salads will soon be on the menus at TGI Friday's and McDonald's.

I don't know about Friday's, but apparently McD's did come out with a kale salad that had more calories than a Big Mac.

Calories (if you haven't been following along, I talked about calories a few days ago) aren't the only indicator of healthiness in a food, but I do find that hilarious.

This makes it pretty interesting that kale and cabbage — along with broccoli, Brussels sprouts, cauliflower, collard greens, and kohlrabi, and several other vegetables — all come from the exact same plant species: Brassica oleracea.

Linguistic detour, as I often do: you might notice that most of those have some variant of "cole" in them. It's in the middle of broccoli, the beginning of cauliflower and collard and kohlrabi, and it's a slight vowel shift for kale. Not so much cabbage itself, but the syllable survives in that version's most perfect presentation, coleslaw. The odd one out is Brussels sprouts. One might be forgiven for thinking that this is where the species name brassica came from, but apparently not; brassica seems to have been Pliny the Elder's name for the cabbage group. No, Brussels sprouts were named for, believe it or not, Brussels, the one in Belgium, near which the plant was heavily cultivated.

Nor was Brussels

apparently named after brassica. The similarity of the first syllables there seems to be another linguistic near-coincidence.

How is this possible? About 2500 years ago, B. oleracea was solely a wild plant that grew along the coast of Britain, France, and countries in the Mediterranean.

Because France doesn't count as "Mediterranean?" I guess they meant the north and/or west coasts of the country.

As for "how is this possible," obviously, the article goes into detail. But it's the same sort of thing as saying "How is it possible that a chihuahua and a Great Dane can be the same species?"

Short version: artificial selection; that is, trait selection by humans. As we, too, are part of nature, the distinction between artificial and natural selection is, well, an artificial one.

For the long version, there's the article.

All this speaks to one thing: the remarkable power of human breeding and artificial selection.

Wow, that could have been worded better, couldn't it? Oh, well; I'm sure I've done worse.

5 Like • Comment • View 2 comments

© 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.