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

December 14, 2020 at 12:17am

#1000204

Nuts To That

"30-Day Blogging Challenge ON HIATUS" [13+]:
14. Roast Chestnuts Day
Every Christmas holiday we all sing about "Chestnuts roasting on an open fire...."
But, have you ever roasted chestnuts!?

"JAFBG" [XGC]:
It's reverse Christmas! You get to steal one thing from someone else and claim it as a gift for yourself. What are you taking?

Who's Chet and why are we roasting his- Oh. CheSTnuts. Clearly, I need glasses. Fortunately, I have an optometrist appointment today. Unfortunately, there is still a fucking pandemic going on.

Speaking of pandemics, 150 years ago, there were billions of chestnut trees in the US. Now there are, like... two? Anyway, here's what happened to them.

. I guess they weren't properly socially distanced.

In colonial America, chestnut was a preferred species for log cabins, especially the bottom rot-prone foundation logs. Later posts, poles, flooring, and railroad ties were all made from chestnut lumber.

I've stayed in cabins featuring the distinctive chestnut wood. It has survived all this time. The actual trees did not. I recall hearing that at one point, American chestnut trees made up as much as 1/3 of the forest of the Blue Ridge Mountains. Don't quote me on that, though; I didn't go looking to verify it.

Despite its decimation as a lumber and nut-crop species...

That word does not mean what they think it means.

Anyway, not only have I never roasted chestnuts, I've never, as far as I can recall, even eaten the little bastards. I've simply never had the opportunity. Sounds like a lot of work. If someone else wants to roast them for me, though, I'd be willing to give it a shot. I also don't know why, other than the song (which I very much want to parody but can't be arsed right now), they're associated with the holiday season, but while I'm at it, what do you mean "we all sing...?"

And the only other line I remember from that song is "Jack Frost nipping at your nose," as if that were some sort of happy thing. No. The cold can go blow itself. All due respect to Nat King Cole (who didn't write it but was the first to perform it), that song sucks worse than most holiday songs.

...I don't have a clever segué into the other prompt today. Steal something to keep as a gift for myself? That sounds like that stupid gods-be-damned White Elephant gift exchange bullshit that I ranted about a few days back. But there's nothing I covet enough to steal, except for maybe a private jet, and even if I did steal that I'd never be able to keep up with the maintenance, insurance, operating costs, etc.

I suppose I could say "All the cash Bezos has in tax-evading offshore accounts." Then I could use that to buy the airplane and maintain it.

But no, I'd still feel bad. It's just not in me to steal, except, you know, writing ideas. "Good writers borrow, great writers steal." Hell, I once accidentally stole a pack of chewing gum from a supermarket. It had fallen between two large boxes that the cashier didn't move while scanning. I was putting my stuff in the car when I noticed this, and my first impulse was, "Go back to the store and pay for this." But then I was like, "It's. A. Pack. Of. Gum."

I'd make a horrible thief.

7 Like • Comment • View 4 comments

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