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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:

Lazy Writer est 4/24/2008

about 21 hours ago
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

a day ago
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

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

August 10, 2019 at 12:23am

#963997

What A Fool Believes

I don't know why I keep going back to this guy's blog.

https://dariusforoux.com/if-you-can-believe-you-can-achieve/

If You Can Believe It, You Can Achieve It

It's generally the epitome of corporate-style motivational affirmations. I'm linking this particular one because he talks about writing, and, well, here we are on a writing site.

I think the world has no shortage of motivational articles, books, videos, or Facebook posts.

You know what motivational quotes make me want to do? Give up. That's what.

Belief is a practical instrument that you can use to shape reality.

No. No, it really isn't. You can use it to shape your attitudes about reality, but reality is reality, by definition, q.e.d., etc.

Have you ever considered that you decide what you believe? Not your friends, colleagues, family, or even the media.

You'd be surprised. There's a whole industry devoted to making sure we believe what someone wants us to believe. Often these beliefs are contradictory. The amazing thing about being human is that we can believe contradictory things simultaneously. This is both a benefit and a detriment.

It comes down to one thing: Do you believe that you can, or can’t live the life you want?

I am living the life that I want. The thing is, it's not necessarily the life that I wanted 10, 20, 30, etc. years ago. Over time, I've adjusted my expectations. I find that that, more than belief, more than motivation, more than anything else, is the secret to happiness. Adjusting expectations meant I could stop, for example, believing that I could invent a flying car, or even own one.

So now we come to the writing part:

I always wanted to become a writer. Back in school, I wrote poems for my girlfriend. It was kind of pathetic, but hey, she enjoyed my weird poems. But all jokes aside, I loved to read and enjoyed putting my thoughts on paper.

But no, every adult in my life was trying to scare me to death. “You can’t make a living as a writer.” They were probably right. It’s not easy to make a living by writing.

True enough. My parents wisely steered me away from creative pursuits so I could make a decent living. "Wisely" for two reasons: 1) it's hard and 2) I'm not very creative.

So what? Everything that’s worth it is hard. I didn’t realize that back then.

That's simply not true, in my experience. The things I appreciate most are the things I didn't work hard for. The harder I work for something, the less satisfying it is - because by the time I'm done putting in the work, it's never as bright as my expectations were.

But, okay, I'll accept that some people feel that way. Fine.

Granted, I’m not fully paying the bills by writing yet. I run a business and do consulting. But I do make some money with my blog. And that’s pretty good to know for the seventeen-year-old version of me.

Meanwhile, I've never made money from writing. Well, that's not entirely true; I suppose Gift Points count, sort of, as do Amazon gift cards - because you can buy stuff with them. I'm not sure I want to make money from blogging; I'd have to take the time to "build a brand" or whatever, and I'd be limited in what I could say.

Sure would be nice to get published, though, but I'm still not convinced that if I just believe hard enough, it'll happen.

Because my mind can conceive it. And if your mind can conceive it, you can achieve it.

That’s not a motivational quote. That’s a fact.

Do you believe it?

No.

My mind can conceive that I'll have a romantic encounter with Halle Berry. It may or may not be that I've put a lot of mental energy into this belief, but let's say for the sake of argument that I have. Will it happen?

No.

My mind can conceive of faster-than-light travel. Could be we'll discover that, one day, but it won't be me doing the discovering, and unless it happens soon, I won't even be around to enjoy the results.

My mind can conceive all sorts of fantastic scenarios, but the closest I'll ever be is if I write a story about them. Worlds made of gold. Time travel. Honest politicians. Flying pigs. Talking cats.

Look, I can accept that attitude makes a difference. But some things are simply unattainable, on a practical level. I've done many things I never thought I'd do, like horseback riding through a jungle and viewing an active volcano. I've also not done many, many more things that I thought I would do, because no, it's not entirely up to me. Sometimes things happen, or they don't happen; you can't make someone fall in love with you, for example.

So I'm not sure why I waste my time with this kind of mind-massage. Maybe I keep hoping that I'll finally read something that is actually applicable to me. Maybe I'm just fascinated by how people - people who are not me, that is - can seem to put whatever New Age word salad on a screen or a page, and get read, while I languish in obscurity.

Obscurity has its benefits, of course, so I can embrace it. At least no one picks apart my verbal vomit, quote by quote, on their own blogs.

Until, at least, someone's analytics finally point them to this blog, at which point I'm probably going to be in big trouble.

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