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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:

GeminiGem of House Lannister

a day ago
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

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

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
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

November 19, 2018 at 1:23am

#945840

Writer's Block

As you probably know, I'm not doing NaNoWriMo this year.

I've had three successful NaNos, meaning I met my 50,000 word goal and got out something that passes for a coherent narrative each time, but I just wasn't feeling it this year.

So, what does it take for me to "feel it?"

Let's take as a given that I want to get more writing done. I mean, I think I'm pretty good at it, and there aren't that many things I'm good at, so it strikes me as something I should want to do. But, as I've explained before, I like to do a lot of things, not just concentrate on one activity (not even video games or drinking, both of which are activities that don't require much creativity).

One thing I've learned from my NaNo experiences: writing, really, isn't about inspiration or motivation; it's about work. It's about getting the words out there, outlining, planning, coming up with characters and situations, and - my personal monster - editing.

So, first, I'd have to get past my aversion to work. I like the easy paths. I may be an adequate writer, but writing is hard. Not physically demanding, at least, but mentally challenging - at least if I'm doing it right, and I demand of myself that I do it right. It's why I don't brew my own beer. Beer is one of my favorite things in the entire universe, but how could I possibly brew a superior beer when there are over 6000 breweries in the US alone, many of which create a delicious amber nectar that I couldn't even hope to approach, let alone surpass? So I'm content to drink those, in the same way that I enjoy reading Brandon Sanderson or Jim Butcher and going, "Okay, there's no way I can ever be that good, so why bother?"

The second thing I need is ideas. Not just one idea. I never do anything for just one reason; that would be inefficient. I think my best work combines two or more ideas and plays them off each other. But I'm not a very creative person by nature, so even coming up with one idea is like hiking up a mountain.

And finally, there's the discipline to sit down and actually do the work, ideally every day. I know I can, because I have, but thinking about doing it again makes me itchy. The worst thing is, I don't know whether I'm more afraid of failure or success. Failure sucks, and success is great, but if there's one lesson that I've truly internalized in life, it's that you can't bring anything new into your life without making room for it by releasing what's already there.

That may be the most difficult part for me: I'm pretty much where I wanted to be in life. But it's a giant Jenga tower: at any time, something could bring it all crashing down if I remove it, but I'm not sure which block will cause the catastrophe. So I keep everything as close to the way it is as I possibly can.

Hell. Probably I need to see a shrink again, although the last one wasn't all that helpful with his "you know, most guys would give their left nut to be where you are right now." Yeah, thanks, I know that; but that doesn't mean there's no room for improvement.

5 Like • Comment • View 6 comments

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