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.

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.

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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.

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.

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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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March 12, 2023 at 12:39pm

#1046275

Revisited: "WTC"

So Daylight Slaving Time has started now. Here, anyway. Not everywhere, thus leading to mass unnecessary confusion.

Speaking of time and confusion, my random generator gave me yet another entry from 2009, part of a series of blog entries expanding upon a list of things to know about Me.

Clear? Good. The entry is "WTC"

.

The bit of Me-trivia at the beginning:

14. I stood atop the World Trade Center when there was a World Trade Center. I don't remember if it had a 13th floor.

Which really doesn't make complete sense unless you know that the previous entry started out with "13. I chuckle whenever I see a building that doesn't have a 13th floor."

I've rambled about 13 fairly recently; no need to bring any of that up again. Back to today's highlighted entry:

Actually, I was there two or maybe three times. Fantastic view when the weather was clear.

At least once as a tourist, and once on business. The tourist thing took me to the observation deck, which was cool. The business thing (I was running errands for my aunt) was actually kind of more interesting, because I got to see parts tourists usually didn't.

Now... there's a link at that site. It's dead. (Actually, both links are dead.) The purpose of the link was to show that I'd discovered that the WTC towers did, indeed, have 13th floors. Before you go saying "See? Obviously it was unlucky," consider this sole surviving quote from the now-dead link:

Both towers of the World Trade Center had occupied 13th floors and, ironically, after hijacked planes slammed into the twin towers on that fateful day, media accounts of harrowing escapes told of many rescues from the 13th floor of both the North (1 World Trade Center) and South (2 World Trade Center) towers.

For those survivors, luck began on the 13th floor.

Well, first of all, actual luck would have involved not having the towers collapse. Second of all, that's flagrant misuse of "ironically." But still, an interesting take on things.

In reality, the number 13 had fuck-all to do with the events. The important thing is that I Was There. Just not on that day. Lucky me.

6 Like • Comment • View 3 comments

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