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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 6 hours 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

about 8 hours 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').

1 Like

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.

May 10, 2021 at 12:15am

#1009954

Some Mother Time

The prompt is running late again, and I can't stay up this time; I have a dentist appointment at some ungodly cow-milking hour tomorrow morning. I'll edit this at some point later today when the 30DBC prompt shows up, but I don't know when; the appointment could take all morning. Nothing major, just a time-consuming procedure.

Just to be clear, I'm not upset about this. It's just I've been sticking to this just-after-midnight schedule for so long that I feel like I should explain when things don't go according to schedule.

So instead, can I just say how damn relieved I am that Mother's Day is finally behind us for another year? Well, 11 months. Mother's Day creep is getting almost as bad as Christmas creep, starting as it does around late March, these days. Not to mention the crass consumerism the days share.

Look, I get it; everyone has a mother, and most of us want to do something to show our appreciation for her labor (of both kinds). Mine died 22 years ago, though, and I really don't appreciate the reminders every goddamn year. No, I'm not trying to make the observance go away for everyone; I'm just trying to minimize my own exposure to it. I keep thinking I should make a filter on my offsite email to send any email containing any variation of "mom" or "mother" straight to the trash, but I can't even be arsed to put that much effort into it. Besides, chances are, I'd end up trashing something relevant among all the pleas to buy this or that product.

Anyway, it's over, and that's probably the last I have to say about it until next year, absent its inclusion in some prompt or other. No promises about not bitching about Father's Day next month, though.

Edit:

PROMPT May 10th

Think back to a time when you felt completely calm. What made you feel that way?

Beer.

No, really. And I don't even have to think back very far. Just about two hours or so.

As I said above, I had dental work done this morning. It took three hours, after which I went home and slept until the local wore off, at which point I felt just fine. So I did my regular weekly pilgrimage to the local taphouse, a bit later than normal so there weren't a lot of other people around.

I sat on the patio, as has been my tradition since this whole bullshit started. The accursed daystar burned in the sky, but it warmed the air enough so the covered patio felt perfectly comfortable. I ordered a beer and a steak salad.

Now, I know that I've described before that feeling that I get when the weather is perfect, I'm drinking beer, and there's good music playing. I call it beerenity. It is, quite simply, the only time when I can pretend that there is nothing wrong in the world, that everything is okay, things are exactly as they should be.

It's a fragile state, so I nurture it while it lasts. There on the patio - I was the only one at the tables - I felt no pain, had no worries, made no plans. It's the closest I ever come to accepting the idea of "living in the present," because everything in that particular moment conspires to make me feel... good.

Calm.

And there's always one moment that triggers it. At some point, some song will play on the sound system and I'll remember, at least in part, all the other moments of beerenity that I've experienced, as if time has no meaning and it all blends together.

In this case, it was this song.

I've been crazy, couldn't you tell?
I threw stones at the stars, but the whole sky fell
Now I'm covered up in straw, belly up on the table
And I drank and sang and passed in the stable on, on

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