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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Turkey DrumStik

about 3 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

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

Nov 14, 2024 at 12:10pm
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

January 3, 2019 at 12:37am

#948760

Fortress of Solitude

Are you an introvert or an extrovert? How do you recharge your batteries?

I don't believe it's binary.

That is, like many other human attributes such as gender and sexual orientation, I'm pretty sure there's a sliding scale. Not that I have any evidence to back it up; only nonscientific observation.

Additionally, the classic portrayal of an introvert is rather unflattering and, worse, inaccurate. "Quiet guy. Kept to himself." They always say that about serial killers after they've been caught, and it makes it sound like that's the cause, rather than them being sociopaths or mentally ill. Mental illness, of course, also isn't an indicator that someone will go on a killing spree.

I've been describing myself as an introvert for years. And, I suppose, given that I do need time alone to recover, I'd fall somewhere on that end of the spectrum. But otherwise, I'm not sure I'd fit the classic profile. I like meeting people. I have a few close friends, but I also have the attitude that almost anyone I meet is a potential friend, and I'm on good terms with a fair number of people that I couldn't consider close friends.

Perhaps it's more that I've simply had to learn to like being alone, because I've had no other choice. I have no siblings (of which I'm aware, anyway). I grew upspent my childhood in a rural area, and the only other kids around, I wasn't allowed to play with. (My parents considered them a bad influence. Their parents considered me a bad influence. Go figure. One of those kids eventually ended up in prison for murder one, so perhaps we were bad influences on each other.)

Anyway, point is, I had to find other ways to distract myself. Endless hours of solitaire. Reading books. Biking alone. Writing terrible poetry. Studying chess. Building model rockets. Making up my own games. When personal computers started to be a thing, I took to them like a moth to the flame. And I did, in fact, enjoy it all. It was only later that I realized that book-reading and game-playing were things that other people only did between social interactions; for me, they were my primary hobbies, interrupted by the tedium of having to deal with people. Still are, in fact.

And yet... in the (unintelligible) years I've been around, I have never managed to live on my own for more than about a month. Always there were parents, then later college roommates, girlfriends, wives, or just friends who needed a place to crash. My work always involved bosses or business partners.

Don't get me wrong; I like my current housemate just fine. We're good friends, and we (mostly) get along in terms of housework as well. Before she started living here, I had other housemates - again, friends who just needed a place to stay. But sometimes I just want to know if I can manage to live alone. Meanwhile, it's a perfectly good arrangement.

The problem with other people is that they bring drama, and I despise drama (outside of fiction, of course). Yes, I know, this probably means that I'm the source of the drama. Whatever; I don't care. Doesn't change how I feel about it. So I limit my time with people.

I usually travel alone. Weeks on the road, just me and my music in a car. Sometimes it'd be nice to have a companion for that, especially when I feel like having a couple of beers, but I wouldn't use someone just as a designated driver. Unless they wanted to get paid. Position's open, by the way.

So, generally, I like most people. I just can't be "on" all the time, so I retreat.

I guess I could take the Myers-Briggs, but the little I know about that has convinced me that I could answer it in such a way as to make it show any result I'd want. Or, more likely, as my perceptions change over time and sometimes day-to-day, even if I answered honestly, I'd have a different result depending on my mood. Or I'd think about how I'd like to be rather than how I am.

Anyway. Point is, I can't really answer that question. Am I actually an introvert, or have I just learned to enjoy self-sufficiency? I suppose it doesn't matter. Functionally, I'm certainly not extroverted. Now, leave me alone.

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