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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10 Most Recent Blog Comments:

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').

1 Like

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

November 27, 2020 at 12:07am

#999190

I Want It Now

The short answer to today's prompt is: Nothing.

PROMPT November 27th

What do you want for Christmas? (Or for your next birthday if you don’t celebrate Christmas)

The long answer (face it, you knew there was going to be a long answer so I could say I wrote an actual blog entry) is that I have enough stuff, including everything I need and most of what I want, and while I appreciate tokens of friendship from people, there's nothing that I can say that I want that most people could afford.

"Stuff," of course, is only part of the big picture, but that's the form most holiday and birthday gifts take, so that's how I approach this.

Last year, the local movie theater / drafthouse was open on Christmas Day, so I decided to start a new Christmas tradition for myself: walk over to the theater, drink all the beer, stagger home. Didn't even see a movie, just drank beer. Then, of course, this happened, and while the theater has reopened, and the beer flows once more, the bar itself is unavailable. I don't know if it'll be open on Christmas Day this year or not.

So much for tradition.

What I want, of course, is what almost everybody wants: this to end. I'm way down on the list of people eligible to get a vaccine when it becomes available, but you can bet your last dollar I'll be getting the jab the moment I can. Am I concerned about them having rushed through the development process? Sure. Am I concerned about side effects? Sure; when I got the shingles vaccine I was useless for two days afterwards. You know what concerns me more than all that? Getting actually sick and possibly passing it on.

That's what a lot of people miss in all this, I think. Sure, you have the choice whether to expose yourself to illness, injury, whatever. Hell, I drink and I smoke cigars. Neither one of those things is going to increase my life expectancy. But when I drink, I don't do things to endanger others. There are laws about not smoking in public places so that secondhand smoke doesn't affect people who haven't made that choice for themselves. We have laws about drunk driving to discourage people from endangering others with the choices they make.

All these restrictions, masks, whatever: they're not just there to protect you from getting sick. They exist so that if you do, you don't pass the illness on to someone who has not made that choice for themselves. By being a selfish prick, you're not "exercising your rights;" you're depriving others of theirs.

Yesterday, I talked about my friend M, and in case you missed it, in the comments I provided an update: M is currently recovering from a stroke. This required hospitalization. Resources that could be used on him are sucked away by pandemic cases, in part because some people have been smug shitstains who absolutely won't be told what to do, and spread the fucking virus.

And this, folks, is why we're doomed. Not because of the pandemic; that will pass. But because of the "screw you I do what I want" mindset. This year has driven home to me that we have absolutely passed the point of no return on climate change. Too many people just will not do the right thing because it's inconvenient. Yes, the world will keep turning. Humanity as a species will survive. But things are going to get pretty rough for a whole lot of people. Displacement, water crises, food shortages, that sort of thing.

So I am working on not caring. I'm done. The assholes win. I can't beat them, so I'm going to join them, and just Do What I Want.

And what I want for Christmas is to drink. I'll manage to do that, whether the drafthouse is open or not.

5 Like • Comment • View 7 comments

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