Complex Numbers (Book)

Blog Calendar

◄ November ► 2022
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:

Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

November 18, 2022 at 12:02am

#1040776

Play It Where It Lies

Hell of a hazard.

A Woman Was Caught Whacking a Golf Ball into the Grand Canyon, and the Feds Aren’t Happy
The latest story of a tourist behaving badly in a national park is a real head scratcher

Source is (shudder) Outside magazine. I still don't know why I keep reading their stuff.

Somewhere in the dark recesses of my memories lives my long-forgotten teenager sensibilities. This is the version of myself that delighted in immature pranks, like toilet papering a classmate’s cottonwood trees and playing ding-dong ditch.

Both of which are annoying but relatively harmless. If no one was injured, a school wasn't evacuated, and nothing caught on fire, you were a goody-two-shoes.

I'm not admitting to anything, by the way. Just saying.

I’ll admit it: my teenaged self would absolutely understand the allure of whacking a golf ball off of the side of the Grand Canyon and watching it disappear into the chasm below.

Okay, so true story: they taught us the basics of golf in sophomore gym class in high school. As I recall, we split up into pairs and each pair got a golf club (don't ask me what its number was or whether it was iron or wood) and a wiffle ball the size of a regulation golf ball. The idea was to learn our swings and recover the ball easily.

I was paired up with the class stoner, who, with a level of perception and intelligence only displayed by a high school stoner, found the one real ball in the box of wiffles. One of each pair of students teed up, and on the coach's command, wound up and swung.

Everyone else's ball caught a bit of air and then dropped down to bounce sadly on the grass. Ours, however, made a perfect golf-ball arc through the air and ended up 300 yards downrange.

Coach got up in our faces. "WAS THAT A REAL BALL?"

Stoner nodded. (Like anyone could have done that with a wiffle.)

"YOU GO GET THAT RIGHT NOW."

So we trudged through the bushes. As soon as we were out of sight, my teammate produced a joint from his pocket and sparked it.

Like I said, perceptive and intelligent.

As I recall, we did find the ball, and both got lousy grades in that gym class. Which was the only class my parents didn't care what grade I got in, so it all worked out for everyone involved. Coach got to get in someone's face; stoner got to get high in class; and I got a story.

Anyway. The relevant thing is that, while I certainly got up to some shady shit in high school, I don't think I ever considered whacking a golf ball off the rim of the Grand Canyon. For one thing, it's 2100 miles away. For another, I don't play golf (it generally requires being *shudder* outside).

On Thursday, National Park Service officials posted an update on the Grand Canyon’s official Facebook page about a woman who filmed herself hitting a golf ball into the canyon, which she then uploaded to TikTok. In the video, the woman also loses the grip on a golf club and flings it off the cliffside.

If it wasn't recorded and posted on social media, it didn't happen.

Now, look. The problem with lofting a golf ball into the Grand Canyon isn't that it might hit someone. The chance of that is infinitesimally small, though admittedly if it did happen the consequences would be terrible. No, it's that it might inspire other people to do it. TokTik trends are a thing, and I can definitely see the "Grand Canyon Hole In One Challenge" going viral. With that many balls flying through the air, the chance of hitting someone increases significantly... as does the amount of litter, which is the real problem here. (The article does mention all this later).

Officials acted swiftly, and with the help of the general public, were able to track down the woman.

Snitches.

At Outside, we come across a litany of stories of people behaving badly in the outdoors, and this year has been a busy one.

More reasons not to go into the outdoors.

There were the high schoolers who booted a football off of Colorado’s Uncompaghre Peak...

Touchdown!

...the dudes who were photographed scrawling graffiti in chalk on a rock at the Grand Canyon...

At least it was chalk and not spray paint?

...and the never-ending march of tourists getting too close to animals at Yellowstone National Park.

Those, I have mixed feelings about. I mean, it might injure the poor animal if it attacks and kills the stupid human, but other than that, it only harms the stupid human. So while it's true that one shouldn't get cuddly with a Yellowstone grizzly, bison, unicorn, or whatever they have out there in the wilderness, the penalty is built right in.

Article doesn't mention my favorite Yellowstone idiocy, which is people who see the pretty pools of azure water and decide to go off the very clearly marked trail festooned with danger signs and warnings (you can't tell me what to do! mah freedumz! stoopid government!) to take a dip. Some of those pools are near boiling and have a pH of like 1.5. Here's someone

of whom nothing was left but a foot.

I mean, that sort of thing is just par for the course.

3 Like • Comment • View 1 comment

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