Complex Numbers (Book)

Blog Calendar

◄ November ►
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 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:

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

November 25, 2024 at 8:41am

#1080466

A Touch of Gray

Today's link is a few years old and from Popular Science, so one shouldn't take it as the final word on the subject. Still an interesting read.

We finally know why stress turns your hair white
Once those strands turn gray, they never go back.

I always figured it was more fright than stress. All the melanocytes just up and run away.

Not really, but I find it amusing.

In 1902, the British Medical Journal reported an unusual case of rapid hair whitening.

A 22-year-old woman “witnessed a tragedy of a woman’s throat being cut and the victim falling dead at her feet,” according to a physician at the London Temperance Hospital. The next day, the right side of her pubic hair turned white, while the left half remained black.

One wonders if that was the inspiration for Cruella de Vil.

And it’s not just random violence that sends people’s pigment running—college exams, children, and work pressure appear to change our coloring, too.

Ah. No wonder I haven't gone gray yet.

But for millennia, scholars have been relying mostly on anecdotal proof and intuition to rationalize this phenomenon. In the absence of clear evidence, many scientists did not believe stress could turn hair snow white, instead arguing the change must be triggered by chemicals or strange immune system behavior.

Right, because stress couldn't possibly change body chemicals or the immune system.

A recent paper, published Wednesday in the journal Nature, may put some of these arguments to rest.

Again, it's not so "recent" anymore. And it's one paper. It's not definitive. That doesn't mean it's wrong.

In the study, stem cell and regenerative biologists from the United States and Brazil reported that stress can indeed cause hair to lose its pigment—and they identified a cellular pathway by which it can occur.

That last bit is, in my view, the important part.

To study this vexing relationship, the researchers created an elaborate animal model, which basically involved trying to turn black-haired rats white with lab-made stressors.

I get why they need to do animal testing for this sort of thing, and stressing out rats isn't going to raise a lot of public ire. Still... poor rats.

Perhaps unsurprisingly, nociception-induced stress, which the scientists stimulated by injecting the rats with resiniferatoxin, an analogue of the chili pepper compound capsaicin, worked best and fastest.

As a sample of one, I can definitively say that overdosing on capsaicin doesn't necessarily turn one's hair white.

Having identified the optimal way to make a rat panic...

Ah, there it is: the phrase at which point I hit "save bookmark."

...the team began searching for corresponding changes in the physiological pathways that give rise to coat color.

There follows more description of the experiment.

Hair still holds many secrets. We don’t know why hair loss plays out differently on someone’s scalp than on their face or, for that matter, their back.

See, I don't mind getting gray hair. Baldness concerns me way more, though I have to admit it would make a few things easier.

In recent years, there’s been a surge in research and development for anti-balding solutions—and many of them show promise. Terskikh, for his part, is working on regenerating hair from scratch using things like pluripotent stem cells. If it works, we’ll have an unlimited supply of hair—presumably in every shade.

Great, just what we need: anime hair, no hair dye necessary.

Won't happen, though. The Manic Panic industry lobby is just too powerful.

5 Like • Comment • View 3 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.