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

January 12, 2021 at 12:02am

#1001916

Fashionating

PROMPT January 12th

What fashion trend makes you cringe or laugh every time you see it? Have you ever wanted to design your own clothing or accessory? What would you design and what features would it have?

Ha! Like I know anything about fashion.

I mean, I am the proud owner of this badge:

Merit Badge in Fashion
[Click For More Info]

Top notch limerick in scroll *^*Bigsmile*^*

But that was a joke presented to me as a joke for a joke.

Now, there are some things that I know are major fashion no-nos, like... um...

I dunno.

Socks with sandals! There. I know one fashion fail.

I'll tell you what I consider the height of fashion, though. My going-out ensemble. This consists of:

A pair of black Levis, regardless of season or temperature. Though sometimes when it's hot I'll substitute a pair of shorts. Men in their 50s shouldn't wear shorts, but men in their 50s also quit giving a shit about what they shouldn't be wearing -- hence why older guys are often seen wearing socks with sandals.

A pair of Birkenstocks (sans socks) -- also regardless of temperature. I've worn these in single-digit weather, outdoors, albeit only for a few minutes. If I go hiking, I'll wear hiking boots, but I'm not going hiking, so Birks it is.

A t-shirt, preferably black. Usually featuring a beer or brewery, or perhaps a musician. Though the one in my portfolio picture is a mashup of Jeff Bridges as The Dude and whatshisname from Tron 2.

An aloha shirt. Because, dammit, Hawaiian shirts are cool and they will never be not cool.

A hat, because fuck you. And not one of those redneck baseball caps, either. Especially not a red one, and definitely not worn with the bill facing backwards like a douchebag.

When the temperature drops below about 54F, a full-length black leather trench coat and a scarf.

I'm fully aware that the combination of a full-length trench and scarf, along with Birkenstock sandals with my toes peeking out, is ridiculous. See the above bullet point about being in my 50s and not giving a shit.

What fashion makes me laugh every time I see it?

Tacti-cool gear. Like what a lot of those shitheads were wearing during the attempted coup on the 6th. Especially -- and I'm not shaming here; we all have our struggles -- but especially if you're overweight; then it becomes military cosplay. (Mad Minotaur Guy, though; sure, he's a deranged lunatic, a terrorist and a traitor, but dude has some fashion sense. It's almost too bad he won't get to express that in prison.)

Yeah, that's right. I just talked about politics in a post about fashion. Deal with it.

But anyway, no, I have neither the desire nor the capability of designing my own line of clothing. if I did, though, it would be something with a lot of pockets, because otherwise I'd have to wear a belt pouch to carry all the different spectacles that I find myself needing at my advanced age, and that would just be wrong.

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