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

1 Like

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

June 18, 2023 at 9:15am

#1051216

Revisited:"Nothing's unforgiven in the four corners of Hell"

It's Time Machine Day, as looking at random posts from the past is what I usually do on Sundays. So I did my usual random number generation, which roped back this post from April of 2010: "Nothing's unforgiven in the four corners of Hell"

Which was, essentially, content-free.

Sorry about that.

Not that I'm above linking videos, but I generally do it as a bonus, not as basically the entire entry.

I remember going to that concert, and I remember I enjoyed it, but apparently I never said another word about it in the blog.

It's been many years since I went to see a concert. This is not because I'm old or introverted; that's never stopped me before. It's also not because of COVID; I quit some time before that mess.

No, it's because of two things:

1) Live Nation / Ticketmaster. "Oh, look, concert tickets are only $125." *goes through the process* "Those tickets just cost me $250."

2) I flat-out refuse to pay for any events at venues named after corporations.

On the first point, if the up-front price had been $250, I might very well have paid it without complaint. But no, they have to add on service charges, convenience fees, venue fees, venue naming rights fees, taxes, the CEOs daughter needs a big wedding fees, overdraft fees, and fuck-you-I'm-a-monopoly charges. They're worse than banks or airlines at this bullshit, and that's saying a lot.

I did read an article recently about how they might stop these deceitful practices, but as far as I'm concerned, the damage has already been done. Screw them.

As for point 2, with all the above excess hidden fees, as well as at-venue advertising and overpriced concessions, you'd think venues would make enough money to keep their names. But no, there's no such thing as "enough money," so they whore out their very identity to some faceless corporation.

One day, if it hasn't been done already (I don't have the intestinal fortitude to look it up) there will be a Live Nation Arena, and hopefully a black hole of corporate greed will form underneath it and suck it into oblivion (while empty, of course; I'm not a monster).

So anyway, that Flogging Molly concert wasn't the last live show I ever attended. I think that was Brandi

Carlile sometime in the mid-tens.

A fine way to end a hobby I used to love.

4 Like • Comment • View 2 comments

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