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.

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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.

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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.

2 Like

June 30, 2024 at 7:40am

#1073352

Revisited: "Rock you like a..."

Today's retrospective takes us back to September of 2018, a brief entry about the weather: "Rock you like a..."

So now, six years less a season later, how have things changed?

It's hard to avoid people talking about the impending doom of Hurricane Florence, so I might as well add my voice to the babble.

I remember that one. While it hit the coast as a Cat 1, it was so slow-moving that what it lacked in wind damage it made up for in massive flooding.

No, I'm nowhere near the coast. Looks like the worst we'll get is a bunch of rain. Nothing new there; it's been raining more often than not all summer. I'm at a high spot and I have a sump pump and a backup generator.

I swear my sense of time is horribly distorted. If you asked me yesterday when I got my generator, I'd have probably answered, "I don't know. 2020, maybe?" Our power sometimes goes out in a light breeze, so it's not just for hurricanes. I justify the presence of the (very loud) generator by claiming I have a medical device that requires electricity, which is true, but the main reason is I don't want to be without internet for more than five minutes.

I also have a house surrounded by trees, though, so I might be boned anyway.

Since then, I've had at least one of the trees taken down, one that was leaning noticeably toward the house. Still boned when the next 'cane blows through.

Some good friends of mine live in Raleigh, NC. They're boned.

They got through it just fine. Couldn't go anywhere for a day or so, if I recall correctly, but safe and dry. They just bought a house in southwest Virginia this year, which means the next hurricane will head for them. And yes, hurricanes can still do significant damage that far inland. Not as often, but it happens.

I have a fondness for Virginia Beach and the Outer Banks. I'll miss them.

My fondness for Virginia Beach ended when I heard that my favorite watering hole there was closing. And miraculously, most of the OBX is still there. I just spent a night there last year.

It seems like a lot of the places I've been to have been hit by something.

Some sort of familiarity bias. Also, I travel more than a little, and every time I do, the chance of a place I've been getting smacked by some disaster goes up a little.

Well, as long as Las Vegas is still- wait, what? The Colorado River is at historic low flows, and Lake Mead is dangerously dry?

Since then, the water level there has fluctuated,

but it's still pretty low. I also haven't been to Vegas since the pandemic started.

I'd ship 'em some of our rain if I could. Let me tell you, if I ever hear another breath about "drought" around here, I'mma lose it at someone.

We've had a bit of a dry spell this year (I write this during a drizzle, however, and we're supposed to get thunderstorms this afternoon and evening). My grass is partly brown. Good thing I don't live in an HOA; I refuse to waste water on lawn irrigation.

They've been predicting a very active hurricane season this year, but those long-range predictions are questionable at best, so I don't pay much attention to them. Weather is notoriously hard to predict with any accuracy more than a week out, so I'll do what I do every year: wait and see.

And try to remember to get my generator serviced.

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