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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Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

November 23, 2020 at 12:01am

#998936

Serial Skiller

Hm... I suppose I'm pretty good at drinking...

PROMPT November 23rd

Write about a time you discovered a new skill in yourself. Or write about the first time you put a new skill into practice.

But no. Actual skill, I suppose.

Thing is, I like to learn stuff -- both theory and practice. But because I like to learn a lot of stuff, I don't excel at any one thing.

I'm sure you know the expression, "Jack of all trades, but master of none?" I've heard it asserted that the original quote ended with "...but oftentimes better than a master of one." I'm sure that makes those of us with broad rather than deep interests feel better, but there's no evidence that this was any sort of "original" version. Maybe it was. Maybe not. I can't be arsed to delve into it much more deeply, which I suppose is fitting. here's the Wiki

, for whatever that's worth.

Thing is, I don't claim to be an expert at anything. Oh, sure, I have training in civil engineering and, I sometimes think, some small facility in writing English, but everything else? Just enough knowledge to be dangerous.

My dad was like that, except he actually did more stuff. He pretty much built our house, with a little bit of help, while I was a kid. It's... not a pretty house, but it's still standing, so I suppose that's something.

Not me, though. First of all, that's too much like work, and second, I wouldn't want to take the chance of shit falling down with me inside. He was apparently okay with the risk, though.

Anyway, I've noted in here before that the latest thing I'm learning is French, so I suppose that counts for the prompt. I still consider myself a beginner, though I can usually muddle through written French and sometimes even translate into the language from English. Don't ask me to speak it, though. My mouth just doesn't want to work that way.

But I suppose you might have also heard the saying that goes something like, "The marvel is not how well the bear dances, but that he dances at all." I've always been told it's very difficult to learn a language at my advanced age. And I wouldn't say it's a cakewalk, but I'm surprising myself by actually learning the words and grammar and so forth. So that's what I discovered in myself - that I don't completely suck at it like I thought I would. It helps to have low expectations of oneself; that way, one can't be too disappointed.

I hope to put it into practice at some point, if I can find someone to help practice it who isn't going to beat me over the head with a day-old baguette for stumbling over the pronunciation. Mostly I just want to see if I can achieve some measure of fluency -- though I'm not holding out a lot of hope for that; I'll settle for being able to ask where I can find the nearest bar. Fortunately, the word for "bar" in French is... "bar."

And hey look, I've come 'round full circle to talk about drinking again.

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