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.

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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.

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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.

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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.

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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.

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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.

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August 6, 2023 at 9:10am

#1053717

Revisited: "Finally!"

Today, we're going all the way back to 2008 for a prototype comment-on-an-external-link format blog entry: "Finally!"

It's short, but as the story is fifteen years old, it's no surprise that the link there is dead. No big deal; I could tell what it was about by the lede I'd copied:

SILVERTON, Ore. -- Management for a popular Silverton restaurant announced Thursday that young children would no longer be allowed into the establishment.

The manager at the Red Thai restaurant on Oak Street said children younger than 6 aren't welcome in the eatery.

Naturally, the questions, here in the future, are obvious: Is there still a Red Thai restaurant on Oak Street in Silverton, Oregon? And if so, is it under the same management? After all, even restaurants without controversial (but excellent) policies close down on a regular basis. Controversy might give them a temporary boost, but they'd have to keep generating more to get such free advertising.

A quick search revealed that, indeed, the Red Thai Room on Oak Street was, sadly, no longer in business. I can't be absolutely certain that "Red Thai Room" and the "Red Thai Restaurant" as mentioned in the news link are the same, but I'd bet money on it. My source? Yelp, which for some reason keeps records like that. There were only two reviews,

both from 2008, on the "recommended" page, both positive, but containing no mention of their wonderful policy.

What I found completely amusing was the dueling reviews on the "not recommended"

page: one one-star bitching about the no-brats rule, and another with five stars singing the praises of the no-brats rule.

Well. The former restaurant, now singing with the choir eternal, was, according to that Yelp page, located at 211 Oak Street. If the review dates are anything to go by, the restaurant, to my great sadness, didn't last long with its glorious policy.

But, if you're ever out that way, apparently there's another restaurant at that same address: Sandee Thai Restaurant.

What an amazing coincidence that the cuisine hasn't changed, but the name has.

Their food looks delicious, by the way, but I'm certainly biased as I love Thai food, or at least what passes for it in the US. The hotter the better. It generally requires some convincing them that, yes, even though I have pale skin, light hair and blue eyes, I love me some Thai spice; but usually, they acquiesce to my request. Though sometimes, they'll stand there with a carton of milk and watch me take the first few bites. Just in case.

I'm not ragging on people who don't tolerate spice well, incidentally. People like what they like. Only on the inherent racism of assuming that I'd be one of them, based on my looks.

And yes, I'm aware of the seeming contradiction between this and my desire not to eat around toddlers. Do not expect me to be consistent, but in this case, it's the difference between someone enjoying their meal in peace, or acting like zoo primates.

Back to my original entry, my words:

But it's nice to think about other restaurants, preferably ones in my area, following suit and denying entry to screaming kids. To me, there's little worse than being at a restaurant and having them seat a kid near me. Even when they're quiet, I end up losing my appetite when I see them eat. I'd rather be near smokers, or even loud drunks.

Sadly, the policy never caught on. Fortunately, my tolerance for the antics of young children in restaurants has increased since then, though if they try to seat me near one, I usually try to obtain a different table. Also fortunately, I'm far more likely, when I'm at home, to order takeout or delivery, thus avoiding both screaming kids and disbelief that a white guy likes his food Thai hot.

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