Complex Numbers (Book)

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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/

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Annette in France

about 3 hours ago
In response to "It's Hot in The South, Once Again!"

The quote is too small and low contrast to be read.

Elycia Lee ☮

about 13 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

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Wordsmitty ✍️

a day ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

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Annette in France

a day ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

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Elisa: Middle Aged Stik

a day ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

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Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

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Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

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Brandiwyn🎶

Sep 25, 2024 at 2:49pm
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

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Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

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Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

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November 21, 2019 at 12:18am

#970130

Money

PROMPT November 21st

What do you value most in a job/career? What about a job makes it satisfying and fulfilling? If you currently hold your “dream job,” what makes it perfect for you? If you are still seeking your dream job, how will you know when you’ve found it? If you are retired, think back to how you felt when you were working.

What do you value most in a job/career?
Money.

What about a job makes it satisfying and fulfilling?
Money.

If you currently hold your “dream job,” what makes it perfect for you?
Money.

If you are still seeking your dream job, how will you know when you’ve found it?
Money.

Okay, so I'm... sort of joking, there? Sort of, but not really.

I would like to think there are some jobs I wouldn't do for any amount of money, but I'm in the fortunate and probably enviable position of being able to pick and choose. I don't mean that I'm above menial labor; if I needed money I'd muck toilet stalls, wash dishes, bus tables, turn big rocks into little ones, pick crops - whatever honest work is still out there and not being done by robots. No, the stuff I wouldn't do for any amount of money would include shady crap like telemarketing (also mostly robots now), promoting pyramid schemes, pump & dump penny stocks. Stuff that makes the world a worse place.

Okay, I probably would violate my principles if you paid me enough. The harsh truth is, I do have a price. It's just a very, very high one. If you want me to do something shady, the remuneration needs to be worth it. If you want me to do something outright illegal, then you need to set me up for life. $2M, minimum. Otherwise it's not worth the potential hit to my freedom and/or reputation. And since I'm not going to trust anyone who offered me that kind of money to keep their promise, I think it's safe to say I won't become a hit man or jewel thief anytime soon.

But none of that is very helpful.

As regular readers know, I identify as an engineer. I went to engineering school. I am technically-minded. But I'm not someone whose identity requires a career. My reason for working really was almost entirely about the money. Yeah, I liked having a visible impact on the world around me, but that also came with a dark side: in spite of regulations and best practices, there was always an environmental price to pay. Point is, a job, to me - even a career - is about making money, not any nebulous "fulfillment" or "satisfaction" or anything like that. I am fulfilled if I have enough money to live in a decent house, eat decent food, and take the occasional vacation. More is nice, too. I get satisfaction from not being hungry. All of this is dependent entirely on money.

People tell me "but money won't keep you warm at night." It literally does.

Anyway, it's all an intellectual exercise because I'm pretty much where I want to be in life, and I'm not about to ruin that by working.

There is only one thing that's bugging me right now, and I'm still not sure what to do about it: I don't have health insurance.

This is not a day-to-day problem for me. I can handle my few check-ups and prescriptions without a problem. The issue is, what if something catastrophic happens? That's what insurance is for, of course, but even if I pay the $850 a month or so (that's the lowest premium I can find on the marketplace, and it carries an enormous deductible), what guarantee do I have that the corporation will actually cover something that happens to me? I hear about peoples' insurance claims being denied all the time.

It's not that I can't afford it. It's that I feel like I'd be better off dedicating that money to a savings account or other safe harbor, rather than gambling on the dubious honesty of profit-motive insurance companies. The best insurance is wealth.

This is only relevant because, for better or worse, insurance wouldn't be an issue if I were still working a professional job. Or, you know, if I lived in a civilized country.

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