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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Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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').

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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.

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.

6 Like • Comment • View 4 comments

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