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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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:

🌕 HuntersMoon

about 3 hours ago
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

a day ago
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

November 14, 2021 at 12:02am

#1021569

Past Tense

PROMPT November 14^th

A Mystery Genre prompt tonight. You are researching your genealogy and find that ancestors from a different generations and different countries made visits to the same remote place. Tell us about this remote place. Why were your ancestors going there?

I don't much care about genealogy.

This is not to say that I think people who do are wrong. Everyone needs a hobby, and if that's yours, great. I'm only talking about my own proclivities here.

I know a bit about my adoptive family's ancestry. They shaped who I am just as surely as genetics must have (when it comes to the ancient nature vs. nurture debate, I'm firmly on the side of "both"). I know about it because my parents, aunts and uncles told me about it. I know, for instance, that my father's mother died when he was very young; later I put two and two together and realized that she was a victim of the Spanish Flu epidemic of the late 1910s / early twenties. I've even tried to find records of them, out of curiosity, but ran into brick walls after grandparents (only one of whom I ever knew, and she died the day after I turned seven). But I didn't care enough to dig deeper.

As for my biological family, I have no interest in finding out about them at all.

I am who I am, and I prefer to think of myself as unbound from any ancestral shackles. Go back far enough, and we all come from the same place anyway.

It always bugs me in shows and movies when a character is like, "Oh, I need to find out who my REAL parents are" when they've been raised by perfectly acceptable human beings, people who cared about them. And they're going to snub all that for the family who gave them away? Rude.

In one of them, the character was a law enforcement official; she discovered that her biological father was a criminal, so she started acting like a criminal because she thought that was a part of who she was. Turns out (plot twist) he wasn't her bio father after all, so that was all her, not genetically programmed.

I know that's just a story, but stories reflect attitudes, and that was an attitude I didn't appreciate.

So, to address the actual prompt, I'll write a story of my own, something I rarely do in this blog, but it fits. The only thing I'll preface this with is to keep in mind that every place on Earth is remote from somewhere.

"So, Dad, I was looking into family history." Ted spooned another morsel of chili into his face.

"Oh?" The older man dabbed his napkin at the corners of his mouth. "Find any skeletons?"

Ted swallowed. "Just one weird thing I don't understand. Seems like everyone on your side was born in Baltimore."

Ted's father leaned back in his chair. "Yep," he acknowledged.

"I was. You were. Your father, his father... not sure about great-grandpa, but even his father was born in Baltimore, and they were still living in England at the time. And we've always lived here in California."

"Well." Dad pressed his lips together. "That's all because of the prophecy."

Ted blinked. "No, really, what's the deal with that?"

"I'm not kidding, son. There was a prophecy. Let's see." His eyes searched the ceiling. "Nope, I don't remember the exact wording. Something about how a son born in Baltimore would one day save the family."

Ted snorted. "Right."

"My dad thought I might be the one, so he took your grandmother to Baltimore to have me. His dad thought he would be the one, so, same deal. And on back as far as I'm aware."

"And none of you fulfilled the prophecy?"

Dad shrugged. "I don't know. Maybe. What exactly is saving the family?"

"Maybe it's about me," said Ted.

It was Dad's turn to snort. "Son, I love you, but you're 45 years old, single, childless, working at Wal-Mart, and living above my garage. You're the last Thistlethwaite. You ain't savin' nothin'. Prophecy's bullshit."

"I'm 47," Ted corrected him.

"Whatever." Dad stood with a grunt and picked up his empty bowl. He headed toward the kitchen. "Doesn't change my point."

"Hey, at least I have a job. What do you do all night while I'm at work, anyway?"

Dad raised his voice from the kitchen. "Sleep, like a normal person. And I worked for thirty damn years to put food on the table for you and your no-good mother."

"You call this food?" Ted mumbled, pushing the chili around the half-empty bowl.

"What was that?"

Ted cleared his throat. "I said, at least Mom could cook."

"You're a disappointment, son."

"You're disappointed now? Wait 'til you see your nursing home."

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