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 11, 2021 at 12:01am

#1021370

Nothing to Go On

I'm almost sorry to go comic on this one, because it's a shitty situation to be in. Er. So to speak.

PROMPT November 11^th

You are desperate to use the bathroom. But, you share this with several others. It's down the hall (waaaay down the hall), and it's cold despite the heat being set to the 'normal' temperature. Being an older person, your legs and ability to hold it ain't what it used to be. How do you handle this dire situation?

Depends.

In a sane world, I'd end this blog entry right there, but we live in the actual world, so I'll just give it a minute for everyone to get that joke.

There are a few benefits to being a dude, and this situation is one of them. I'm reminded of an old joke:

Adam and Eve are chilling in the Garden one day when God appears. "Hey, listen," he says. "I'm almost done here, just have two things left to Create. And I figured I'd give one to each of you."

They nod. "That's fair."

"Okay." He checks his notes. "First we have: the ability to pee standing up."

Adam jumps up and raises his hand. "Ooh! Ooh! Oh, man, that would be awesome. I could be out in the fields and, boom, just let go right where I am. Pick me, pick me!"

God looks at Eve. She shrugs.

"Okay, that one's all yours, Adam." God makes a check mark on the list. "And finally, we have: multiple orgasms."

Where I went to college, not far from where I live now, one of the greatest honors bestowed upon a fourth-year student who had great grades and participated in many different activities (e.g., not me) is to live in the original lodging at the University, rooms designed by Thomas Jefferson himself and built in the early 1800s. As these rooms predated many modern conveniences, none of them include bathrooms; one has the honor of going outside, along a covered but otherwise very open walkway, down a steep flight of stairs, and into a communal restroom/shower. And in case you don't know, it gets cold in central Virginia in the winter.

The Lawn rooms (for that is what they're called) do have sinks, but the rules forbade Lawnies from using the sink for anything apart from hand-washing and teeth-brushing, even during the cold and sleety season.

People being people, that rule was frequently broken. Hence a graffito I saw in an actual restroom near the Lawn one day while I was enrolled there:

Roses are red
Violets are pink
If you can't find a toilet
Pee in the sink

None of which is very useful to about half the population, though. Or the other half about 1/4 of the time. But keep in mind that indoor plumbing is fairly new as far as civilization is concerned, and for a lot of our history, they mostly used, essentially, buckets.

Therefore, to prepare for the situation described in the prompt, one of my priority purchases would be a bucket. I mean, if you want to get fancy about it, this thing

goes for about 20 bucks new (and I don't want to know what it sells for on the used market).

It'd be the only thing on the list, really. An actual, literal bucket list.

8 Like • Comment • View 5 comments

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